# Find the gcf of each set of numbers 150, 200, and 300

## Answers

4, 8, 10, 7, 3, 4... Those r in order from top to bottom! it's all about the simplification!

1. factors of 14 are = 1, 2, 7, 14...

factors of 35 are = 1, 5, 7, 35...

therefore, the greatest common factor is going to be 7.

2. factors of 24 are = 1, 2, 3, 4, 6, 8, 12, 24...

factors of 45 are = 1, 3, 5, 9, 15, 45...

Therefore, the greatest common factor is 3.

3. factors of 25 are = 1, 5, 25

factors of 32 are = 1, 2, 4, 8, 16, 32

Therefore, the greatest common factor is 1.

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Divisors of 18 are 1, 2, 3, 6, 9, 18.

Divisors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.

The largest number on both lists is 6. This is the GCF of 18 and 24.

a) No. The number present must be a divisor of 6.

b) Yes. The number present is a divisor of 6.

c) The number present must be a divisor of 6.

d) Possible numbers present are 1, 2, 3, 6.

It isn't clear what "make a list" means in this context. It is customary to find the GCF in any of several ways, only a couple of which involve making lists. Here, we will list the prime factors, then form the product of the common ones. (Here, each pair of numbers has only one common factor.)

1. 14 = 2·7, 35 = 5·7. GCF(14, 35) = 7

2. 24 = 2³·3, 45 = 3²·5. GCF(24, 45) = 3

3. 25 = 5², 32 = 2⁵. GCF(25, 32) = 1

The GCF is 6

Step-by-step explanation:

12/6=2

30/6=5

72/6=12

all are divisible by the greatest # of 6.

The question asks for the GCF of 18 and 24, then the common factors between both numbers. Remember that the GCF and all factors can only be integers for this question.

Find all of the common factors of 18 and 24:

Factors of 18: {1,2,3,6,9,18}

Factors of 24: {1,2,3,4,6,8,12,24}

Common factors are bolded. The common factors between 18 and 24 are 1, 2, 3, and 6. The greatest common factor is 6.

a.

It is impossible for 5 members to be present, as 5 is not a common factor.

b.

It is possible for 3 members to be present, as 3 is a common factor.

c.

The number of members must be a common factor between 18 and 24, as that allows for the books to be divided equally between the common factor amount of members.

d.

The possible numbers of members present can be 1, 2, 3, or 6 members.

It is 6 for both of them 60: 1 2 3 4 5 6 20 12 20 30 60

24: 1 2 3 4 6 8 12 24

The GCF is 12

Factors of 24: 1, 24, 2, 12, 3, 8, 4, 6

Factors of 60: 1, 60, 2, 30, 3, 20, 5, 12

7

Step-by-step explanation:

Lets make an orginzed way to search through

14 - - -(1*14)(2*7)

(1,2,7,14)

35 - - -(1*35)(5*7)

(1,5,7,35)

84 - - -(1*84)(2*42)(3*28)(4*21)(6*14)(7*12)

the greatest common factor here is 7

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GCF for 3 is 6.

GCF for 4 is 18.