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