Question

Where is Euclid's division lemma used in daily life

Answer 1

Euclid’s Division Lemma states that for any given positive integers a and b, there exists unique integers q and r such that a = bq + r, where 0 ≤ r < b

In mathematics Lemma cannot be proved. They can be veriáed. 
Suppose a number let say 53 is divided by 5, then what are the quotient and remainders obtained?

The quotient is 10 and the remainder is 3 (Note: the remainder is always less than the divisor. Here the divisor is 5, and the dividend is 53)

Thus, we can write 53 = 5 × 10 + 3
 i.e. for a = 53 and b = 5, we obtain q = 10 and r = 3.