Question

Find the HCF and LCM of:
117, 221

Answer 1

Step 1: Prime Factorization

Divide by 3: 117 ÷ 3 = 39

Divide 39 by 3: 39 ÷ 3 = 13

13 is a prime number.

So, the prime factorization of 117 is:
117 = 3² × 13¹

Divide by 13: 221 ÷ 13 = 17

17 is a prime number.

So, the prime factorization of 221 is:

221 = 13¹ × 17¹

Step 2: Finding HCF

The HCF is found by taking the lowest power of all common prime factors. 

The common prime factor between 117 and 221 is 13.

The lowest power of 13 in both factorizations is 13¹.

Thus, the HCF is:
HCF = 13

Step 3: Finding LCM

The LCM is found by taking the highest power of all prime factors present in either number.

From 117: 3² and 13¹

From 221: 13¹ and 17¹

Now, we take the highest powers:

3² from 117

13¹ from both

17¹ from 221

Thus, the LCM is:

LCM = 3² × 13¹ × 17¹

LCM = 9 × 13 × 17

9 × 13 = 117

117 × 17 = 1989

Thus, the LCM is:

LCM = 1989

HCF of 117 and 221 is 13.

LCM of 117 and 221 is 1989.