Question

Find the HCF of 1260 and 7344 using Euclid’s algorithm.

Answer 1

Hint: We have to find the HCF of 1260 and 7344 using Euclid’s algorithm. In Euclid’s algorithm we have to keep on dividing unless the remainder is not zero. If the remainder is not zero then the divisor becomes the dividend and the remainder becomes the divisor.

Complete step-by-step answer:
We are given two numbers 1260 and 7344 and we are asked to find the HCF of the numbers using Euclid’s algorithm.
As 7344 > 1260, so we divide 7344 by 1260.
7344/1260 = 5 with remainder as 1044.
As the remainder is not 0, we divide 1260 by 1044.
1260/1044 = 1 with remainder as 216.
As the remainder is not 0, we divide 1044 by 216.
1044/216 = 4 with remainder as 180.
As the remainder is not 0, we divide 216 by 180.
216/180 = 1 with remainder as 36.
As the remainder is not 0, we divide 180 by 36.
180/36 = 5 with remainder as 0.
Since, the remainder is now 0,
The HCF of 7344 and 1260 is 36.

Note: In Euclid’s algorithm we use the concept of long division. Here we continue the division until the remainder becomes zero. It is also known as GCD (Greatest common Divisor), which means the greatest common number which when divides both the numbers, gives the remainder as zero.