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Question

Find the greatest common factor of 31 and 93.(1 point)
The greatest common factor of 31 and 93 is
.

Answer 1

To find the greatest common factor (GCF) of 31 and 93, we can start by recognizing that 31 is a prime number. This means it only has two factors: 1 and 31 itself.

Next, let's examine the number 93. We can factor 93 as follows:

93 ÷ 3 = 31 Thus, 93 = 3 × 31.

The only common factor between 31 and 93 is 31 itself.

So, the greatest common factor of 31 and 93 is 31.

Answer 2

double check （￣︶￣）↗　:-P

Answer 3

Sure, let’s double-check the calculations for the greatest common factor (GCF) of 31 and 93.

1. Factors of 31: Since 31 is a prime number, its only factors are 1 and 31.

2. Factors of 93:

   • To find the factors of 93, we can check for its divisibility.
   • 93 can be divided by 3 (since 9+3=12, which is divisible by 3):
     • \( 93 \div 3 = 31 \)
   • Therefore, 93 can be factored as \( 3 \times 31 \).
   • The factors of 93 are 1, 3, 31, and 93.

Now, comparing the factors:

• Factors of 31: 1, 31
• Factors of 93: 1, 3, 31, 93

The common factors are 1 and 31.

Thus, the greatest common factor (GCF) of 31 and 93 is indeed 31.

You were correct! (￣︶￣)↗

Answer 4

A toddler has 36 blocks, of which 16 are blue and 20 are pink. They want to sort the blocks so that each group has both colors of blocks. The toddler also wants each group to have an equal number of blue blocks and an equal number of pink blocks. Which answer best shows how the toddler should sort the blocks using the GCF and the Distributive Property of multiplication over addition?(1 point)
Responses

2(8+10)
2 left parenthesis 8 plus 10 right parenthesis

4(4+5)
4 left parenthesis 4 plus 5 right parenthesis

1(16+20)
1 left parenthesis 16 plus 20 right parenthesis

4(4×5)

Answer 5

To solve this problem, we need to determine the greatest common factor (GCF) of the blue and pink blocks so that each group has both colors in equal amount.

1. Number of Blue Blocks: 16
2. Number of Pink Blocks: 20

Next, we find the GCF of 16 and 20:

• Factors of 16: 1, 2, 4, 8, 16
• Factors of 20: 1, 2, 4, 5, 10, 20

The common factors are 1, 2, and 4. Therefore, the GCF is 4.

Now, if the toddler wants equal groups with both colors of blocks, and since the GCF is 4, we can divide the total blocks by 4:

• For blue blocks: \[ \frac{16}{4} = 4 \]
• For pink blocks: \[ \frac{20}{4} = 5 \]

This tells us that each of the 4 groups will have 4 blue blocks and 5 pink blocks.

Now we can express this using the distributive property:

• The total number of blocks in one group can be expressed as: \[ 4 \text{ groups} \times (4 \text{ blue} + 5 \text{ pink}) = 4(4 + 5) \]

Thus, the correct response from the given options is:

4(4 + 5).

Answer 6

At a school cafeteria, a staff person surveyed the food preferences of 35 students. For every five students, two said they liked healthy foods. How many students preferred healthy foods?(1 point)
Responses

12
12

14
14

4
4

16

Answer 7

To find out how many students preferred healthy foods based on the given information, we can use the ratio provided:

For every 5 students, 2 said they liked healthy foods.

1. Total students surveyed: 35
2. Ratio of students who like healthy foods: For every 5 students, 2 like healthy foods.

Next, we can find out how many groups of 5 can be formed from 35 students: \[ \frac{35}{5} = 7 \text{ groups} \]

Since each group has 2 students who prefer healthy foods: \[ 7 \text{ groups} \times 2 \text{ (healthy food preference per group)} = 14 \text{ students} \]

Therefore, the number of students who preferred healthy foods is 14.

So, the correct answer is:

14.

Answer 8

here are 40 students in Joan’s class. She plans to invite them to her birthday party. She asked them to suggest a theme for her party. Three of every eight students suggested a rainbow-themed party. How many students suggested a rainbow-themed party? How many did not?(1 point)
students suggested a rainbow-themed party, while
students did not.

Answer 9

To find out how many students suggested a rainbow-themed party, we can use the given ratio of students who suggested this theme.

1. Total number of students: 40
2. Ratio of students suggesting a rainbow theme: 3 out of every 8 students.

Now, we can calculate the number of students who suggested the rainbow theme:

• First, we find how many groups of 8 are in 40 students: \[ \frac{40}{8} = 5 \text{ groups} \]

Since each group has 3 students suggesting a rainbow-themed party: \[ 5 \text{ groups} \times 3 \text{ (students per group)} = 15 \text{ students} \]

So, 15 students suggested a rainbow-themed party.

Now, to find out how many students did not suggest a rainbow-themed party: \[ 40 \text{ (total students)} - 15 \text{ (students who suggested rainbow)} = 25 \text{ students} \]

Thus:

• 15 students suggested a rainbow-themed party.
• 25 students did not.

In summary:

• 15 students suggested a rainbow-themed party, while 25 students did not.

Answer 10

Mary ate 412
pears and Carmie ate 724
pears. If they finished all the pears in a box, how many pears were in the box?(1 point)
Responses

1114
11 Start Fraction 1 over 4 End Fraction

12
12

1136
11 Start Fraction 3 over 6 End Fraction

11

Answer 11

To find out how many pears were in the box, we need to add the number of pears Mary ate to the number of pears Carmie ate.

• Mary ate 412 pears.
• Carmie ate 724 pears.

Now, we will add these two numbers together:

\[ 412 + 724 = 1136 \]

So, the number of pears in the box is 1136.

Thus, the correct response is:

1136.