Question

Hcf of 105,84,42 by prime factorization using short division method

Answer 1

Answer: 21

Step-by-step explanation

Refer to the diagram shown below. The numbers 105, 84, and 42 are written in the first row. Next to that list is the prime 3 which is a factor of all 3 values (use the divisibility by 3 rule to confirm this).

Then,

• 105/3 = 35
• 84/3 = 28
• 42/3 = 14

This explains why the numbers 35, 28, and 14 are in the next row. The 7 next to it is a factor of all three values, and,

• 35/7 = 5
• 28/7 = 4
• 14/7 = 2

The next row 5,4,2 have no factors in common other than 1. Therefore we stop at this point.

The highlighted primes of 3 and 7 multiply to 3*7 = 21 which is the HCF.