Question

Determine the largest number which divides 204 and 472 leaving remainder 3 in each case

Answer 1

Answer: we need 3 as reminder so subtract 3 from both digits:

204-3=201

472-3=469

Find HCF for both the values

HCF(201,469) = 67

Answer 2

we have to determine the largest number which divides 204 and 472 leaving remainder 3 in each case.

Let largest number is x.

x divides 204 and 472 leaving remainder 3 in each case.

it means, x divides (204 - 3) = 201 and (472 - 3) = 469 without leaving remainder.

now, for finding largest value of x , find highest common factor of 201 and 469.

so, x = HCF { 201, 469}

prime factors of 201 = 3 × 67

prime factors of 469 = 7 × 67

so, HCF of 201 and 469 = highest common factor of 201 and 469 = 67.

hence, value of x = 67.

so, 67 is the largest number which divides 204 and 472 leaving remainder 3in each case.