Question

Find the largest number which divides 546 and 764 leaving remainders 6 and 8 respectively

Answer 1

546-6=540
764-8=756
then find HCF of
540=2²×3³×5
756=2²×3³×7

2×2×3×3×3=108
Therefore answer is 108

Answer 2

$\fontsize{18}{10}{\textup{\textbf{The largest number is 108.}}}$

Step-by-step explanation:

The largest number that divides 546 and 764 leaving remainders 6 and 8 respectively is given by

highest common factor of 546 – 6 = 540 and 764 – 8 = 756.

The prime factorization of  540 and 756 are

540 = 2 × 2 × 3 × 3 × 3 × 5 = 2² × 3³ × 5

and

756 = 2 × 2 × 3 × 3 × 3 × 7 = 2² × 3³ × 7

∴ HCF = 2² × 3³ = 108  

Hence, the largest number is 108.

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Question : Find the largest number which divides 546 and 764 leaving remainders 6 and 8 respectively.

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