Common Factors

COMMON FACTORS:

Factors that, two or more numbers have in common are called common factors.

Find the Common factors of the numbers:

1) 12 and 36.

Answer:

We need to find the factors of the two given numbers separately and have to find the factors that are in common in both the numbers.

12 = 1*12 =  2*6 = 3*4.

36 = 1*36 = 2*18 = 3*12 = 4*9 = 6*6.

(i) Factors of number 12:  1, 2, 3, 4, 6, and 12.

(ii) Factors of number 36: 1, 2, 3, 4, 6, 9, 12, 18, and 36.

Here, the factors that are common in both the given numbers are:

Common factors: 1, 2, 3, 4, 6, and 12.

 

2) 18 and 57.

Answer:

18 = 1*18 = 2*9 = 3*6.

57 = 1*57 = 3*19.

(i) Factors of number 18:  1, 2, 3, 6, 9, and 18.

(ii) Factors of number 57: 1, 3, 19, and 57.

Therefore, Common factors: 1, 3.

 

3) 10, 25 and 60.

Answer:

10 = 1*10 = 2*5.

25 = 1*25 = 5*5.

60 = 1*60 = 2*30 = 3*20 = 4*15 = 5*12 = 6*10.

(i) Factors of number 10: 1, 2, 5, and 10.

(ii) Factors of number 25:  1, 5, and 25.

(iii) Factors of number 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.

Therefore, Common factors : 1,  5.

4) 12, 18 and 36.

Answer:

12 = 1*12 = 2*6 = 3*4.

18 = 1*18 = 2*9 = 3*6.

36 = 1*36 = 2*18 = 3*12 = 4*9 = 6*6.

(i) Factors of number 12:  1, 2, 3, 4, 6, and 12.

(ii) Factors of number 18: 1, 2, 3, 6, 9, and 18.

(iii) Factors of number 36: 1, 2, 3, 4, 6, 9, 12, 18 and 36.

Therefore, Common factors: 1, 2, 3, 6.