# Using Euclid’s algorithm, find the HCF of (i) 405 and 2520 (ii) 504 and 1188 (iii) 960 and 1575

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Using Euclid’s algorithm, find the HCF of

(i) 405 and 2520

(ii) 504 and 1188

(iii) 960 and 1575

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(i)

On applying Euclid’s algorithm, i.e. dividing 2520 by 405, we get:

Quotient = 6, Remainder = 90

∴ 2520 = 405 × 6 + 90

Again on applying Euclid’s algorithm, i.e. dividing 405 by 90, we get:

Quotient = 4, Remainder = 45

∴ 405 = 90 × 4 + 45

Again on applying Euclid’s algorithm, i.e. dividing 90 by 45, we get:

∴ 90 = 45 × 2 + 0

Hence, the HCF of 2520 and 405 is 45.

(ii)

On applying Euclid’s algorithm, i.e. dividing 1188 by 504, we get:

Quotient = 2, Remainder = 180

∴ 1188 = 504 × 2 + 180

Again on applying Euclid’s algorithm, i.e. dividing 504 by 180, we get:

Quotient = 2, Remainder = 144

∴ 504 = 180 × 2 + 144 Again on applying Euclid’s algorithm, i.e. dividing 180 by 144, we get:

Quotient = 1, Remainder = 36

∴ 180 = 144 × 1 + 36

Again on applying Euclid’s algorithm, i.e. dividing 144 by 36, we get:

∴ 144 = 36 × 4 + 0

Hence, the HCF of 1188 and 504 is 36.

(iii)

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.