Question

if a=3^2*5^3*7, b=5^2*7^2*3,c=7^3*5 and HCF (a,b,c) = 5^n*7*3^m , then n= ________ , m=_______
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Answer 1

Step-by-step explanation:

a = 3² × 5³ × 7

b = 5² × 7² × 3

c = 7³ × 5

Simplification of above term :

a = (3² × 5²) × 35

a = 15² × 35

b = (5×7)² × 3

b = 35² × 3

c = (7×5)×7²

c = 7² × 35

*(Since 35 is a common term we will seperate it out and include it in as one of our term in H. C. F for the next step)

After seperating : a = 15² = 225 , b = 105 , c = 49

Since the H. C. F of 225,105 and 49 is 1, 35 is the H. C. F of a, b and c.

H. C. F(a, b, c) = 5ⁿ × 7 × 3^m

Equation : 5ⁿ × 7 × 3^m = 35

: 5ⁿ × 3^m = 5¹ × 3^0

After equating powers, we get the values of 'n' and 'm' as 1 and 0 respectively.

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