Step: 1

Draw a factor tree for each number.

Step: 2

20 = 5 × 2 × 2

32 = 2 × 2 × 2 × 2 × 2

32 = 2 × 2 × 2 × 2 × 2

[Write the prime factorization for each number.]

Step: 3

Identify the common factors.

Step: 4

2 × 2 = 4

[Multiply the common factors.]

Step: 5

The GCF of 20 and 32 is 4.

Correct Answer is : 4

Step: 1

Draw a factor tree for each number.

Step: 2

24 = 3 × 2 × 2 × 2

40 = 5 × 2 × 2 × 2

40 = 5 × 2 × 2 × 2

[Write the prime factorization for each number.]

Step: 3

[Identify the common factors.]

Step: 4

2 × 2 × 2 = 8

[Multiply the common factors.]

Step: 5

The GCF of 24 and 40 is 8.

Correct Answer is : 8

Step: 1

If a number is the GCF of any two numbers, then the two numbers are multiples of that GCF.

Step: 2

1 x 5 = 5

2 x 5 = 10

2 x 5 = 10

[Write the first two multiples of 5.]

Step: 3

The two smallest numbers whose GCF is 5 are 5 and 10.

Correct Answer is : 5 and 10

Step: 1

The prime factorisation of 72 and 84 are:

72 = 2^{3} × 3^{2}

84 = 2^{2} × 3 × 7

72 = 2

84 = 2

Step: 2

H.C.F. is found by multiplying all the prime factors having the least powers.

Step: 3

Therefore, the H.C.F. of 72 and 84 = 2^{2} × 3 = 12.

Correct Answer is : 12

Step: 1

While using Long Division Method for finding H.C.F. of two numbers, follow these steps:

(1) Divide the larger number by the smaller number.

(2) Divide the divisor by the remainder.

(3) Repeat the process of dividing until you get remainder as 0.**The divisor which gives remainder 0 is the H.C.F.**

(1) Divide the larger number by the smaller number.

(2) Divide the divisor by the remainder.

(3) Repeat the process of dividing until you get remainder as 0.

Step: 2

Using the long division method, we get the H.C.F. of 1824 and 2304 as follows:

Step: 3

In the division above, the divisor 84 gives remainder 0. Therefore, the H.C.F. of 1764 and 2604 is 84.

Correct Answer is : 84

Step: 1

H.C.F. of three numbers = H.C.F. of [(H.C.F. of any two) and the third.]

Step: 2

First we find the H.C.F. of any two of the given numbers.

Step: 3

While using Long Division Method for finding H.C.F. of two numbers, follow these steps:

(1) Divide the larger number by the smaller number.

(2) Divide the divisor by the remainder.

(3) Repeat the process of dividing until you get remainder as 0.**The divisor which gives remainder 0 is the H.C.F.**

(1) Divide the larger number by the smaller number.

(2) Divide the divisor by the remainder.

(3) Repeat the process of dividing until you get remainder as 0.

Step: 4

First, let us find the H.C.F. of 714 and1666. Using the long division method, we get the H.C.F. of 714 and 1666 as follows:

Step: 5

In the division above, the divisor 238 gives remainder 0. Therefore, the H.C.F. of 714 and 1666 is 238.

Step: 6

Repeat the same process for the remaining number and the divisor **238** which got the remainder as 0.

Step: 7

Using the long division method, we get the H.C.F. of 238 and 9775 as follows:

Step: 8

In the division above, the divisor 17 gives remainder 0. Therefore, the H.C.F. of 238 and 9775 is 17.

Step: 9

Hence, the H.C.F. of 714, 1666 and 9775 is 17.

Correct Answer is : 17

Step: 1

The prime factorisation of 630, 576 and 1080 are:

630 = 2 × 3^{2} × 5 × 7

576 = 2^{6} × 3^{2}

1080 = 2^{3} × 3^{3} × 5

630 = 2 × 3

576 = 2

1080 = 2

Step: 2

H.C.F. is found by multiplying all the prime factors having the least powers.

Step: 3

Therefore, the H.C.F. of 630, 576 and 1080 = 2 × 3^{2} = (2 × 9) = 18.

Correct Answer is : 18

Step: 1

The prime factorisation of 1965, 1755 and 1560 are:

1965 = 3 × 5 × 131

1755 = 3^{3} × 5 × 13

1560 = 2^{3} × 3 × 5 × 13

1965 = 3 × 5 × 131

1755 = 3

1560 = 2

Step: 2

H.C.F. is found by multiplying all the prime factors having the least powers.

Step: 3

Therefore, the H.C.F. of 1965, 1755 and 1560 = 3 × 5 = 15.

Correct Answer is : 15

Step: 1

The prime factorisation of 972 and 432 are:

972 = 2^{2} × 3^{5}

432 = 2^{4} × 3^{3}

972 = 2

432 = 2

Step: 2

H.C.F. is found by multiplying all the prime factors having the least powers.

Step: 3

Therefore, the H.C.F. of 972 and 432. = 2^{2} × 3^{3} = (4 × 27) = 108.

Correct Answer is : 108

Step: 1

List all the factors of the numbers.

Factors of 7: 1 and 7

Factors of 21: 1, 3, 7 and 21

Factors of 7: 1 and 7

Factors of 21: 1, 3, 7 and 21

Step: 2

Select the common factors.

Factors of 7: 1 and 7

Factors of 21: 1, 3, 7 and 21

Factors of 7: 1 and 7

Factors of 21: 1, 3, 7 and 21

Step: 3

Among the common factors 1 and 7, the greatest common factor is 7.

Step: 4

Therefore, the greatest common factor of 7 and 21 is 7.

Correct Answer is : 7

Step: 1

List all the factors of the numbers.

Factors of 40: 1, 2, 4, 5, 8, 10, 20 and 40

Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.

Factors of 40: 1, 2, 4, 5, 8, 10, 20 and 40

Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.

Step: 2

Select the common factors.

Factors of 40: 1, 2, 4, 5, 8, 10, 20 and 40.

Factors of 48: 1, 2, 4, 6, 8, 12, 16, 24 and 48

Factors of 40: 1, 2, 4, 5, 8, 10, 20 and 40.

Factors of 48: 1, 2, 4, 6, 8, 12, 16, 24 and 48

Step: 3

Among the common factors 1, 2, 4 and 8, the greatest common factor is 8.

Step: 4

Therefore, the greatest common factor of 40 and 48 is 8.

Correct Answer is : 8

Step: 1

Multiplying 1 and 8, we get the value as 8.

[The smallest number is 1 and the GCF is 8.]

Step: 2

Multiplying 2 and 8, we get the value as 16.

[The second smallest number is 2 and the GCF is 8.]

Step: 3

8 = 1, 8

16 = 1, 2, 8, 16

16 = 1, 2, 8, 16

[Write the factors for the two values 8 and 16.]

Step: 4

Select the common factors.

Step: 5

8 and 16 are the two smallest possible numbers with GCF 8.

Correct Answer is : 8 and 16

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