Question

How to find the largest number which divides 735 and 1155 leaving no remainder

Answer 1

by using euclid's division lemma
a = bq +r ( 0_< r < b )
where a = dividend
b = divisor
q = quotient
and r = remainder

Answer 2

735=5×7×7×3:1155=5×7×3×11:

Thus the HCF of 735 and 1155 is 5×7×3=105.

Therefore, the largest number is 105.

HCF (Highest Common Factor) : The largest positive integer, a number which is a divider of   two or more integer numbers with zero remainder is named as  Highest Common Factor (HCF).

The HCF is the highest number that divides exactly into two or more numbers.

When we find all the factors of two or more numbers, and some factors are "common", then the largest one  is the Greatest Common Factor.

Abbreviated "GCF"