Exam 4: Number Theory

Classify as true or false, assuming that a, b, c, and d are whole numbers an $\mathrm { d } \neq 0$ - $\text { If } \mathrm { d } \nmid a b \text {, then } \mathrm { d } \nmid a \text {. }$

(True/False)

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(78)

Question 41

Solve the problem. -If a bag of jellybeans has 105 jellybeans, what is the greatest number of bowls that can be filled with 35 jellybeans?

(Multiple Choice)

4.7/5

(77)

Question 42

Determine all possible digits to place in the square that make the statement true. If none exist, state this. - $4,3 \square 0 \text { is divisible by } 6 \text {. }$

(Short Answer)

4.7/5

(90)

Question 43

Without using a calculator, determine whether the first number is divisible by the second number. -Is 198,819 divisible by 9?

(Multiple Choice)

4.7/5

(84)

Question 44

Determine all possible digits to place in the square that make the statement true. If none exist, state this. - $4,3 \square 1 \text { is divisible by } 3 \text {. }$

(Short Answer)

4.9/5

(80)

Question 45

Solve the problem. -If a group of 238 people is to be split into equal-sized subgroups of at least two people and no more than 30 people, what are the possible numbers of groups?

(Multiple Choice)

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(58)

Question 46

Find the LCM for the given numbers by an appropriate method. - $9 ^ { 10 }$ and $49^{10}$

(Multiple Choice)

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(91)

Question 47

Using divisibility tests, solve the problem. -Reuben is planting a large garden filled with corn. Can he plant 136 corn plants in 8 equal rows?

(Multiple Choice)

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(83)

Question 48

If a number is divisible by 5, then every digit of the number is divisible by 5.

(True/False)

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(81)

Question 49

Find the prime factorization. -229

(Multiple Choice)

4.8/5

(90)

Question 50

Provide the appropriate response. -Find the least positive number divisible by two primes.

(Multiple Choice)

4.9/5

(76)

Question 51

Without using a calculator, determine whether the first number is divisible by the second number. -Is 927,441 divisible by 5?

(Multiple Choice)

4.8/5

(71)

Question 52

Classify as true or false, assuming that a, b, c, and d are whole numbers an $\mathrm { d } \neq 0$ - $\text { If } \mathrm { d } \mid \mathrm { a } \text { and } \mathrm { d } \mid \mathrm { b } \text {, then } \mathrm { d } \mid ( \mathrm { ax } + \mathrm { by } ) \text { for any whole numbers } x \text { and } y \text {. }$

(True/False)

4.9/5

(85)

Question 53

Find the GCD for the given numbers by an appropriate method. -176 and 189

(Multiple Choice)

4.8/5

(73)

Question 54

Use least common multiple or greatest common divisor to solve the problem. -Three clocks chime every 21 minutes, 39 minutes, and 91 minutes, respectively. If the three clocks chime together, how much time must pass before they will chime together again?

(Multiple Choice)

4.9/5

(91)

Question 55

$\text { If } \operatorname { GCD } ( \mathrm { a } , \mathrm { b } ) = \mathrm { a } \text {, then } a \mid b \text {. }$

(True/False)

4.9/5

(74)

Question 56

Without using a calculator, determine whether the first number is divisible by the second number. -Is 85,104,901 divisible by 11?

(Multiple Choice)

5.0/5

(77)

Question 57

Classify as true or false, assuming that a, b, c, and d are whole numbers an $\mathrm { d } \neq 0$ - $\text { If } \mathrm { d } \nmid ( \mathrm { a } + \mathrm { b } ) \text {, then } \mathrm { d } \nmid \mathrm { a }$

(True/False)

4.8/5

(89)

Question 58

If a number is divisible by 8, then it is also divisible by 16.

(True/False)

4.7/5

(93)

Question 59

Solve the problem. -Jack has 82 trees that he wants to plant in a rectangular array. List the possible arrays.

(Multiple Choice)

4.9/5

(70)

Question 60

Classify as true or false, assuming that a, b, c, and d are whole numbers an $\mathrm { d } \neq 0$ - $\text { If } \mathrm { d } \nmid a b \text {, then } \mathrm { d } \nmid a \text {. }$

Solve the problem. -If a bag of jellybeans has 105 jellybeans, what is the greatest number of bowls that can be filled with 35 jellybeans?

Determine all possible digits to place in the square that make the statement true. If none exist, state this. - $4,3 \square 0 \text { is divisible by } 6 \text {. }$

Without using a calculator, determine whether the first number is divisible by the second number. -Is 198,819 divisible by 9?

Determine all possible digits to place in the square that make the statement true. If none exist, state this. - $4,3 \square 1 \text { is divisible by } 3 \text {. }$

Solve the problem. -If a group of 238 people is to be split into equal-sized subgroups of at least two people and no more than 30 people, what are the possible numbers of groups?

Find the LCM for the given numbers by an appropriate method. - $9 ^ { 10 }$ and $49^{10}$

Using divisibility tests, solve the problem. -Reuben is planting a large garden filled with corn. Can he plant 136 corn plants in 8 equal rows?

If a number is divisible by 5, then every digit of the number is divisible by 5.

Find the prime factorization. -229

Provide the appropriate response. -Find the least positive number divisible by two primes.

Without using a calculator, determine whether the first number is divisible by the second number. -Is 927,441 divisible by 5?

Find the GCD for the given numbers by an appropriate method. -176 and 189

Use least common multiple or greatest common divisor to solve the problem. -Three clocks chime every 21 minutes, 39 minutes, and 91 minutes, respectively. If the three clocks chime together, how much time must pass before they will chime together again?

$\text { If } \operatorname { GCD } ( \mathrm { a } , \mathrm { b } ) = \mathrm { a } \text {, then } a \mid b \text {. }$

Without using a calculator, determine whether the first number is divisible by the second number. -Is 85,104,901 divisible by 11?

Classify as true or false, assuming that a, b, c, and d are whole numbers an $\mathrm { d } \neq 0$ - $\text { If } \mathrm { d } \nmid ( \mathrm { a } + \mathrm { b } ) \text {, then } \mathrm { d } \nmid \mathrm { a }$

If a number is divisible by 8, then it is also divisible by 16.

Solve the problem. -Jack has 82 trees that he wants to plant in a rectangular array. List the possible arrays.

An Introduction to Problem Solving

Introduction to Logic and Sets

Numeration Systems and Whole Number Operations

Integers

Rational Numbers and Proportional Reasoning

Rational Numbers As Decimals and Percents

Real Numbers and Algebraic Thinking

Probability

Data Analysisstatistics: an Introduction

Introductory Geometry

Congruence and Similarity With Constructions

Congruence and Similarity With Transformations

Area, Pythagorean Theorem, and Volume

Filters

Exam 4: Number Theory

Classify as true or false, assuming that a, b, c, and d are whole numbers an d≠0\mathrm { d } \neq 0d=0 - If d∤ab, then d∤a. \text { If } \mathrm { d } \nmid a b \text {, then } \mathrm { d } \nmid a \text {. } If d∤ab, then d∤a.

Solve the problem. -If a bag of jellybeans has 105 jellybeans, what is the greatest number of bowls that can be filled with 35 jellybeans?

Determine all possible digits to place in the square that make the statement true. If none exist, state this. - 4,3□0 is divisible by 6. 4,3 \square 0 \text { is divisible by } 6 \text {. }4,3□0 is divisible by 6.

Without using a calculator, determine whether the first number is divisible by the second number. -Is 198,819 divisible by 9?

Determine all possible digits to place in the square that make the statement true. If none exist, state this. - 4,3□1 is divisible by 3. 4,3 \square 1 \text { is divisible by } 3 \text {. }4,3□1 is divisible by 3.

Solve the problem. -If a group of 238 people is to be split into equal-sized subgroups of at least two people and no more than 30 people, what are the possible numbers of groups?

Find the LCM for the given numbers by an appropriate method. - 9109 ^ { 10 }910 and 491049^{10}4910

Using divisibility tests, solve the problem. -Reuben is planting a large garden filled with corn. Can he plant 136 corn plants in 8 equal rows?

If a number is divisible by 5, then every digit of the number is divisible by 5.

Find the prime factorization. -229

Provide the appropriate response. -Find the least positive number divisible by two primes.

Without using a calculator, determine whether the first number is divisible by the second number. -Is 927,441 divisible by 5?

Find the GCD for the given numbers by an appropriate method. -176 and 189

Use least common multiple or greatest common divisor to solve the problem. -Three clocks chime every 21 minutes, 39 minutes, and 91 minutes, respectively. If the three clocks chime together, how much time must pass before they will chime together again?

If GCD⁡(a,b)=a, then a∣b. \text { If } \operatorname { GCD } ( \mathrm { a } , \mathrm { b } ) = \mathrm { a } \text {, then } a \mid b \text {. } If GCD(a,b)=a, then a∣b.

Without using a calculator, determine whether the first number is divisible by the second number. -Is 85,104,901 divisible by 11?

Classify as true or false, assuming that a, b, c, and d are whole numbers an d≠0\mathrm { d } \neq 0d=0 - If d∤(a+b), then d∤a\text { If } \mathrm { d } \nmid ( \mathrm { a } + \mathrm { b } ) \text {, then } \mathrm { d } \nmid \mathrm { a } If d∤(a+b), then d∤a

If a number is divisible by 8, then it is also divisible by 16.

Solve the problem. -Jack has 82 trees that he wants to plant in a rectangular array. List the possible arrays.

An Introduction to Problem Solving

Introduction to Logic and Sets

Numeration Systems and Whole Number Operations

Integers

Rational Numbers and Proportional Reasoning

Rational Numbers As Decimals and Percents

Real Numbers and Algebraic Thinking

Probability

Data Analysisstatistics: an Introduction

Introductory Geometry

Congruence and Similarity With Constructions

Congruence and Similarity With Transformations

Area, Pythagorean Theorem, and Volume

Filters

Classify as true or false, assuming that a, b, c, and d are whole numbers an $\mathrm { d } \neq 0$ - $\text { If } \mathrm { d } \nmid a b \text {, then } \mathrm { d } \nmid a \text {. }$

Determine all possible digits to place in the square that make the statement true. If none exist, state this. - $4,3 \square 0 \text { is divisible by } 6 \text {. }$

Determine all possible digits to place in the square that make the statement true. If none exist, state this. - $4,3 \square 1 \text { is divisible by } 3 \text {. }$

Find the LCM for the given numbers by an appropriate method. - $9 ^ { 10 }$ and $49^{10}$

$\text { If } \operatorname { GCD } ( \mathrm { a } , \mathrm { b } ) = \mathrm { a } \text {, then } a \mid b \text {. }$

Classify as true or false, assuming that a, b, c, and d are whole numbers an $\mathrm { d } \neq 0$ - $\text { If } \mathrm { d } \nmid ( \mathrm { a } + \mathrm { b } ) \text {, then } \mathrm { d } \nmid \mathrm { a }$