Question

Using Euclid division algorithm find the largest number which divides 870 and 258 leaving remainder 3 in each case.(CBSE Board 2020).

Answer 1

Answer: 51

Step-by-step explanation:

a=870-3=867

b=258-3=255

a=bq+r

867=255*3+102

255=102*2+51

102=51*2+0

HCF =51

Answer 2

Given:

Two number are 870 and 258. Remainder is 3.

To Find:

Using Euclid division algorithm find the largest number which divides 870 and 258 leaving remainder 3 in each case.

Solution:

On subtracting remainder from both number:

First number = 870 - 3 = 867

Second number = 258 - 3 = 255

H.C.F of first and second number can be find out from Euclid division algorithm:

a = b ×q + r

Where a is dividend , b is divisor, q is quotient and r is remainder. It must follow:    

0≤ r < b

H.C.F of 867 and 255:

867 = 3 × 255 + 102

255 = 2 × 102 + 51

102 = 2× 51 + 0

So H.C.F of 867 and 255 is 51:

51 will be the largest number which divides 870 and 258 leaving remainder 3 in each case.