Highest Common Factor of 666, 665 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 666, 665 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 666, 665 is 1 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 666, 665 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 666, 665 is 1.

HCF(666, 665) = 1

HCF of 666, 665 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 666, 665 is 1.

Highest Common Factor of 666,665 using Euclid's algorithm

Highest Common Factor of 666,665 is 1

Step 1: Since 666 > 665, we apply the division lemma to 666 and 665, to get

666 = 665 x 1 + 1

Step 2: Since the reminder 665 ≠ 0, we apply division lemma to 1 and 665, to get

665 = 1 x 665 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 666 and 665 is 1

Notice that 1 = HCF(665,1) = HCF(666,665) .

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Frequently Asked Questions on HCF of 666, 665 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 666, 665?

Answer: HCF of 666, 665 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 666, 665 using Euclid's Algorithm?

Answer: For arbitrary numbers 666, 665 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.