1.

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

Answer»

We know the required number divides 540 (546 – 6) and 756 (764 – 8), respectively. 

∴ Required largest number = HCF (540, 756) 

Prime factorization: 

540 = 2 × 2 × 3 × 3 × 3 × 5 = 22 × 32 × 5 

756 = 2 × 2 × 3 × 3 × 3 × 7 = 22 × 32 × 7 

∴ HCF = 22 × 33 = 108 

Hence, the largest number is 108.

We know the required number divides 540 (546 – 6) and 756 (764 – 8), respectively. 

∴ Required largest number = HCF (540, 756) 

Prime factorization: 

 540 = 2 × 2 × 3 × 3 × 3 × 5 = 22 × 32 × 5 

756 = 2 × 2 × 3 × 3 × 3 × 7 = 22 × 32 × 7 

∴ HCF = 22 × 33 = 108 

Hence, the largest number is 108



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