Question

How to find the common factors and H.C.F of 20, 35, and 40​

Answer 1

he instructions to find the LCM of 20, 35 and 40 are the next:

1. Decompose all numbers into prime factors

20 2 10 2 5 5 1

35 5 7 7 1  

40 2 20 2 10 2 5 5 1  

2. Write all numbers as the product of its prime factors

Prime factors of 20 = 22 . 5

Prime factors of 35 = 5 . 7

Prime factors of 40 = 23 . 5

3. Choose the common and uncommon prime factors with the greatest exponent

Common prime factors: 5

Common prime factors with the greatest exponent: 51

Uncommon prime factors: 2 , 7

Uncommon prime factors with the greatest exponent: 23, 71

4. Calculate the Least Common Multiple or LCM

Remember, to find the LCM of several numbers you must multiply the common and uncommon prime factors with the greatest exponent of those numbers.

LCM = 51. 23. 71 = 280

Answer 2

The factors of 20 are 1, 2, 4, 5, 10, 20

The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30

The factors of 45 are 1, 3, 5, 9, 15, 45

Hence the common factors are only 1 and 5.

The highest common factors in this case is only 5.

Hope this helps : )