Question

Using Euclid’s algorithm, find the HCF of

960 and 1575

Answer 1

On applying Euclid’s algorithm, i.e. dividing 1575 by 960, we get: 

Quotient = 1, Remainder = 615 

∴ 1575 = 960 × 1 + 615 

Again on applying Euclid’s algorithm, i.e. dividing 960 by 615, we get: 

Quotient = 1, Remainder = 345 ∴ 960 = 615 × 1 + 345 

Again on applying Euclid’s algorithm, i.e. dividing 615 by 345, we get: 

Quotient = 1, Remainder = 270 

∴ 615 = 345 × 1 + 270 

Again on applying Euclid’s algorithm, i.e. dividing 345 by 270, we get: 

Quotient = 1, Remainder = 75 

∴ 345 = 270 × 1 + 75 

Again on applying Euclid’s algorithm, i.e. dividing 270 by 75, we get: 

Quotient = 3, Remainder = 45 

∴ 270 = 75 × 3 + 45 

Again on applying Euclid’s algorithm, i.e. dividing 75 by 45, we get: 

Quotient = 1, Remainder = 30 

∴ 75 = 45 × 1 + 30 

Again on applying Euclid’s algorithm, i.e. dividing 45 by 30, we get: 

Quotient = 1, Remainder = 15 

∴ 45 = 30 × 1 + 15 

Again on applying Euclid’s algorithm, i.e. dividing 30 by 15, we get:

Quotient = 2, Remainder = 0 

∴ 30 = 15 × 2 + 0 

Hence, the HCF of 960 and 1575 is 15.