Greatest Common Factor

Greatest common factor is the greatest number which is a common factor of two or more number.

There is no difference between highest common factor (H.C.F) or greatest common divisor (G.C.D) or greatest common factor (G.C.F).

1. Find the greatest common divisor (G.C.D) of 70, 210 and 315?

Solution:

Factors of 70 = 1, 2, 5, 7, 10, 14, 35, and 70.

Factors of 210 =1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, and 210.

Factors of 315 =1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, and 315. Therefore, common factor of 70, 210 and 315 = 1,5, 7 and 35.

Greatest common divisor (G.C.D) of 70, 210 and 315= 35.

2. Find the greatest common divisor (G.C.D) of 60, 90 and 150?

Solution:

Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.

Factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45 and 90.

Factors of 150 = 1,2, 3, 5, 6, 10, 15, 25, 30, 50, 75 and 150.

Therefore, common factor of 60, 90 and 150 = 1, 2, 3,5, 6,10, 15 and 30.

Greatest common divisor (G.C.D) of 60, 90 and 150 = 30.

3. What is the highest common factor (H.C.F) of 56 and 91?

Solution:

Factors of 56 = 1, 2, 4, 7, 8, 14, 28 and 56.

Factors of 91 = 1, 7, 13, and 91.

Therefore, common factor of 56 and 91 = 1and 7.

Highest common factor (H.C.F) of 56 and 91 = 7.

4. What is the greatest common factor (G.C.F) of 24 and 66?

Solution:

Factors of 24 = 1, 2, 3, 4, 6, 8, 12, and 24.

Factors of 66 =1, 2, 3, 6, 11, 22, 33 and 66.

Therefore, common factor of 24 and 66 = 1, 2, 3 and 6.

Greatest common factor (G.C.F) of 24 and 66 = 6.

5.What is the highest common factor (H.C.F) of 51 and 111?

Solution:

Factors of 51 = 1, 3, 17 and 51.

Factors of 111 =1, 3, 37, and 111.

Therefore, common factor of 51 and 111 = 1and 3.

Highest common factor (H.C.F) of 51 and 111 = 3.

6.What is the greatest common factor (G.C.F) of 11 and17?

Solution:

Factors of 11 = 1 and 11.

Factors of 17 =1 and 17.

Therefore, common factor of 11 and 17 = 1.

Greatest common factor (G.C.F)of11 and 17 = 1.