Question

What great number can divide 696 and 531 leaving a remainder 3

Answer 1

Answer:

33

Step-by-step explanation:

Let n be the number that we want.

Since 696 divided by n leaves a remainder of 3, the number n is a divisor of 696-3 = 693.

Since 531 divided by n leaves a remainder of 3, the number n is a divisor of 531-3 = 528.

So n is a common divisor of both 693 and 528.  Since we want the greatest such number, n is the greatest common divisor (GCD; also called the HCF) of 693 and 528.

The prime factorizations of these numbers are:

693 = 3² × 7 × 11

528 = 2⁴ × 3 × 11

From here, the GCD of 693 and 528 is 3 × 11 = 33.

Thus n = 33 is the greatest number that leaves a remainder of 3 when divided into 696 and 531.