Question

Find the hcf of 196 and38220

Answer 1

Answer:

HCF of 196 and 38220 is 195

Step-by-step explanation:

According to Euclid's lemma is a = bq +r

a=38220 , b =195

38220 = (196 ×195)+0

Since remainder = 0

Hence,

HCF of 196 and 38220 is 195

Answer 2

Given:

196 and 38220

To be found:

HCF of 196 and 38220

Prime factorization of both the numbers,

$\begin{array}{r | l}2 & 196\\\cline{2-2} 2 & 98 \\\cline{2-2} 7 & 49 \\\cline{2-2} 7 & 7 \\\cline{2-2} & 1 \\\end{array}$     196 = 2⁴ × 7⁴

and

$\begin{array}{r | l}2 & 38220 \\\cline{2-2} 2 & 19110 \\\cline{2-2} 5 & 9555 \\\cline{2-2} 3 & 1911 \\\cline{2-2} 7 & 637 \\\cline{2-2} 13 & 91 \\\cline{2-2} 7 & 7 \\\cline{2-2} & 1\end{array}$       38220 = 2² × 3 × 5 × 7² × 13

So,

196 = 2⁴ × 7⁴

38220 = 2² × 3 × 5 × 7² × 13

For finding HCF find common in between the numbers and choose the lowest power.

we get 2² × 7² = 4 × 49 = 196

Hence

HCF(38220, 196) = 196