Examples of Greatest Common Factor

Examples of greatest common factor or highest common factor or greatest common divisor are discussed here.

In greatest common factor (G.C.F)or highest common factor (H.C.F) or greatest common divisor (G.C.D), we know that there is no difference between them.

1. What is the greatest common factor (G.C.F) of 96 and 64?

Solution:

Factors of 96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48 and 96.

Factors of 64 =1, 2, 4, 8, 16, 32 and 64.

Therefore, common factor of 96 and 64 = 1, 2, 4,8, 16 and 32.

Greatest common factor (G.C.F) of 96 and 64 = 32.

2. What is the greatest common factor (G.C.F) for 32 and 80?

Solution:

Factors of 32 = 1, 2, 4, 8, 16 and 32.

Factors of 80 =1,2,4,5,8,10,16, 20 and 80.

Therefore, common factor of 32 and 80= 1, 2, 4,8 and 16.

Greatest common factor (G.C.F) of 32 and 80 = 16.

3. Find the greatest common divisor (G.C.D) of 16 and 30?

Solution:

Factors of 16 = 1, 2, 4, 8 and 16.

Factors of 30 = 1, 2, 3, 5, 6, 10, 15 and 30. Therefore, common factor of 16 and 30 = 1 and 2.

Greatest common divisor (G.C.D) of 16 and 30 = 2.

4. Find the greatest common divisor (G.C.D) of 45 and 120?

Solution:

Factors of 45 = 1, 3, 5, 9, 15, and 45.

Factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120.

Therefore, common factor of 45 and 120 = 1, 3,5 and 15.

Greatest common divisor (G.C.D) of 45 and 120 = 15.

5. What is the highest common factor (H.C.F) of 8 and 12?

Solution:

Factors of 8 = 1, 2, 4 and 8.

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

Therefore, common factor of 8 and 12 = 1, 2and 4.

Highest common factor (H.C.F) of 8 and 12 = 4.

6. What is the highest common factor (H.C.F) of 360 and 210?

Solution:

Factors of 360 = 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 and 360.

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

Therefore, common factor of 360 and 210= 1, 2, 3,5, 6, 10, 15 and 30.

Highest common factor (H.C.F) of 360 and 210 = 30.

7. What is the highest common factor (H.C.F) of 36, 54 and 63?

Solution:

Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18 and 36.

Factors of 54 = 1, 2, 3, 6, 9, 18, 27, and 54.

Factors of 63 =1, 3, 7, 9, 21, and 63.

Therefore, common factor of 36, 54 and 63 = 1, 3 and 9.

Highest common factor (H.C.F) of 36, 54 and 63 = 9.

8. What is the greatest common factor (G.C.F) of 10 and 300?

Solution:

Factors of 10 = 1, 2, 5 and 10.

Factors of 300 =1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150 and 300.

Therefore, common factor of 10 and 300 = 1, 2, 5 and 10.

Greatest common factor (G.C.F) of 10 and 300 = 10.

9. Is 1 the greatest common factor (G.C.F) of 11 and 300?

Solution:

Factors of 11 = 1 and 11.

Factors of 300 =1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150 and 300.

Therefore, common factor of 11 and 300 = 1.

Greatest common factor (G.C.F) of 11 and 300 = 1.

Yes, 1 is the greatest common factor (G.C.F) of 11 and 300.

10. What is the greatest common factor (G.C.F) of 39and 78?

Solution:

Factors of 39 = 1, 3, 13 and 39.

Factors of 78 = 1, 2, 3, 6, 13, 26, 39 and 78.

Therefore, common factor of 39 and 78 = 1, 3,13 and 39.

Greatest common factor (G.C.F) of 39 and 78 = 39.