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.