We included **HMH Into Math Grade 4 Answer Key**** PDF** **Module 10 Lesson 2 Identify Factors** to make students experts in learning maths.

## HMH Into Math Grade 4 Module 10 Lesson 2 Answer Key Identify Factors

I Can use division to determine whether a number is a factor of another number.

**Spark Your Learning
**1. Mrs. Aisha owns a bakery. She wants to put all of these blueberry muffins in a display case with the same number of muffins on each shelf. Which display case should Mrs. Aisha use?

Use visual models to support your answer.

Answer:

Display case Mrs. Aisha should use = 4 shelves because in 3 shelves they cannot fit correctly.

Explanation:

Number of blueberry muffins she has = 16.

Multiples of 16:

1 × 16 = 16.

2 × 8 = 16.

4 × 4 = 16.

Number of muffins on each shelf = 4 selves = 4 × 4.

**Turn and Talk** Why can putting 16 objects in 3 and 4 equal rows help you know whether 3 or 4 is a factor of 16?

Answer:

Putting 16 objects in 3 and 4 equal rows can help to know whether 3 or 4 is a factor of 16 because it can be divisible by that number.

Explanation:

Multiples of 16:

1 × 16 = 16.

4 × 4 = 16.

**Build Understanding
**Question 1.

Mrs. Aisha makes a new kind of granola bar for her customers to try. She wants to display 40 bars in equal rows on a tray. Can Mrs. Aisha place all the bars in 5 equal rows?

Use a visual model to represent the problem.

A. What shape does your visual model show? ______

B. What does this shape tell you about whether or not all the granola bars can be placed in equal rows?

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C. Can Aisha put all the granola bars in 5 rows? How does your visual model show this?

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D. Is 5 a factor of 40? How do you know?

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Answer:

Yes, Mrs. Aisha can place all the bars in 5 equal rows.

Explanation:

Number of bars in equal rows on a tray she wants to display = 40.

Mrs. Aisha place all the bars in 5 equal rows.

Multiples of 40:

1 × 40 = 40.

2 × 20 = 40.

4 × 10 = 40.

5 × 8 = 40.

**Turn and Talk** Why can you write a division equation and a multiplication equation to model this problem?

Answer:

We can write a division equation and a multiplication equation to model this problem, because both are same to find how many bars comes in five rows as we know the total bars count.

Explanation:

We can write a division equation and a multiplication equation to model this problem, because both are same to find how many bars comes in five rows as we know the total bars count.

2. Mrs. Aisha has 35 loaves of French bread. She wants to put the same number of loaves in 3 baskets. Can she put all the loaves in the baskets with none left over?

A. Why can you use division to solve this problem?

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B. Complete the division. Show your work.

C. Can all the loaves be put in 3 baskets with the same number in each basket? How do you know?

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D. Is 3 a factor of 35? How do you know?

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Answer:

11 baskets Loaves can be kept and 2 will be remaining.

Explanation:

Number of loaves of French bread Mrs. Aisha has = 35.

Number of loaves in baskets she wants to put the same = 3.

Factors of 3: 3,6,9,12,15,18,21,24,27,30,33,36.

35 is not a factor of 3.

Hence, in 11 baskets they can be kept and 2 will remain.

**Connect to Vocabulary**

A factor of a number divides that number evenly. The quotient is a whole number and the remainder is 0.

**Turn and Talk** How does using division to find factors of a number relate to using an array or area model to find factors of a number?

Answer:

We can use division to find factors of a number relate to using an array or area model to find factors of a number by division method.

Explanation:

Arrays are useful models for multiplication which can be used in a variety of ways, ranging from highly structured lessons to games and open investigations. An array is formed by arranging a set of objects into rows and columns. Each column must contain the same number of objects as the other columns, and each row must have the same number as the other rows.

**Step It Out
**3. Is 6 a factor of 84?

Use divisibility rules to answer and explain.

Connect to Vocabulary

A number is divisible by a second number if the quotient is a whole number and the remainder is 0. So, if a number is divisible by , then is a factor of that number.

A. Is 84 divisible by 2? _____

B. Is 84 divisible by 3? _____

C. Is 84 divisible by 6? ____

D. Is 6 a factor of 84? _____

Answer:

So, if a number is divisible by 2 and 3, then 6 is a factor of that number.

Yes, 6 is a factor of 84.

Explanation:

A. 84 divisible by 2:

=> 84 is even, Hence 84 is divisible by 2.

b. 84 divisible by 3.

Sum of digits = 8 + 4 = 12.

=> 3 × 4 = 12.

Hence, 84 is divisible by 3 because sum of digits is a multiple of 3.

C. 84 divisible by 6.

Sum of digits = 8 + 4 = 12.

=> 2 × 6 = 12.

3 × 4 = 12.

84 is divisible by 6 because it is divisible by 2 and 3.

D. 6 a factor of 84.

Multiples of 6:

6,12,18,24,30,36,482,48,54,60,66,72,78,84.

**Check Understanding Math Board
**Question 1.

Mrs. Aisha wants to put 51 bagels in bins, with the same number in each bin. Should she use 3 or 4 bins? Use factors to justify your answer.

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Answer:

she should use 3 bins to put 51 bagels in bins, with the same number in each bin.

Explanation:

Number of bagels in bins Mrs. Aisha wants to put = 51.

Multiples of 51:

1 × 51 = 51.

3 × 17 = 51.

3 is a factor of 51 not 4.

**On Your Own
**Question 2.

**Use Tools**There are 26 members in the marching band. Can all the members march in 4 equal rows?

- Use square tiles to represent the problem. Then draw an array to show your work.
- Can 26 band members march in 4 equal rows? Use factors or divisibility to explain.

Answer:

4 is not the factor of 26. They cannot march in 4 equal rows.

Explanation:

There are 26 members in the marching band.

All the members march in 4 equal rows.

=> Multiples of 26:

1 × 26 = 26.

2 × 13 = 26.

**Use a visual model to answer and explain.
**Question 3.

Is 6 a factor of 32?

Answer:

No, 32 is not a factor of 6.

Explanation:

Multiples of 32:

1 × 32 = 32.

2 × 16 = 32.

4 × 8 = 32.

Question 4.

Is 5 a factor of 25?

Answer:

Yes, 5 a factor of 25.

Explanation:

Multiples of 25:

1 × 25 = 25.

5 × 5 = 25.

Question 5.

**Use Repeated Reasoning** Explain whether or not the following statement is true: Since 89 is not divisible by 2, then 89 is not divisible by any multiple of 2.

Answer:

Yes, the following statement is true because 89 cannot be divided by any factor of 2 as 89 is not an even number.

Explanation:

89 is not divisible by 2, then 89 is not divisible by any multiple of 2.

**On Your Own
**Question 6.

**Use Structure**There are 72 students in the after-school program. They will play one of the sports listed in the table. The program leader wants all the students to be on a team and all the teams to have the same number of players. Which sport should they play? Why?

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Answer:

Volley ball sport they should play because number of players on each team 9 in 12 teams.

Explanation:

Number of students in the after-school program = 72.

Multiples of 72:

1 × 72 = 72.

2 × 36 = 72.

3 × 24 = 72.

4 × 18 = 72.

6 × 12 = 72.

8 × 9 = 72.

**Use division to answer and explain.
**Question 7.

Is 7 a factor of 91?

Answer:

Explanation:

91 ÷ 7 = 13.

Question 8.

Is 8 a factor of 94?

Answer:

Explanation:

94 ÷ 8 = 11\(\frac{6}{8}\)

**Use divisibility rules to answer and explain.
**Question 9.

Is 5 a factor of 80?

________________

________________

Answer:

Yes, 5 is a factor of 80.

Explanation:

Multiples of 80:

1 × 80 = 80.

2 × 40 = 80.

4 × 20 = 80.

5 × 16 = 80.

8 × 10 = 80.

Question 10.

Is 9 a factor of 88?

________________

________________

Answer:

No, 9 is not a factor of 88.

Explanation:

Factors of 88:

1 × 88 = 88.

2 × 44 = 88.

4 × 22 = 88.

8 × 11 = 88.

**I’m in a Learning Mindset!
**How effective was using division to determine whether or not a number is a factor of another number?

Answer:

Division helps in easy calculation to know whether the number is divisible by so and so number. That means to determine whether or not a number is a factor of another number.

Explanation:

The division is the process of sharing a collection of items into equal parts and is one of the basic arithmetic operations in math’s.