Highest Common Factor of 660, 645 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 660, 645 i.e. 15 the largest integer that leaves a remainder zero for all numbers.

HCF of 660, 645 is 15 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 660, 645 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 660, 645 is 15.

HCF(660, 645) = 15

HCF of 660, 645 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 660, 645 is 15.

Highest Common Factor of 660,645 using Euclid's algorithm

Highest Common Factor of 660,645 is 15

Step 1: Since 660 > 645, we apply the division lemma to 660 and 645, to get

660 = 645 x 1 + 15

Step 2: Since the reminder 645 ≠ 0, we apply division lemma to 15 and 645, to get

645 = 15 x 43 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 660 and 645 is 15

Notice that 15 = HCF(645,15) = HCF(660,645) .

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Frequently Asked Questions on HCF of 660, 645 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 660, 645?

Answer: HCF of 660, 645 is 15 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 660, 645 using Euclid's Algorithm?

Answer: For arbitrary numbers 660, 645 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.