Highest Common Factor of 821, 668 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 821, 668 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 821, 668 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 821, 668 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 821, 668 is 1.

HCF(821, 668) = 1

HCF of 821, 668 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 821, 668 is 1.

Highest Common Factor of 821,668 using Euclid's algorithm

Highest Common Factor of 821,668 is 1

Step 1: Since 821 > 668, we apply the division lemma to 821 and 668, to get

821 = 668 x 1 + 153

Step 2: Since the reminder 668 ≠ 0, we apply division lemma to 153 and 668, to get

668 = 153 x 4 + 56

Step 3: We consider the new divisor 153 and the new remainder 56, and apply the division lemma to get

153 = 56 x 2 + 41

We consider the new divisor 56 and the new remainder 41,and apply the division lemma to get

56 = 41 x 1 + 15

We consider the new divisor 41 and the new remainder 15,and apply the division lemma to get

41 = 15 x 2 + 11

We consider the new divisor 15 and the new remainder 11,and apply the division lemma to get

15 = 11 x 1 + 4

We consider the new divisor 11 and the new remainder 4,and apply the division lemma to get

11 = 4 x 2 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 821 and 668 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(15,11) = HCF(41,15) = HCF(56,41) = HCF(153,56) = HCF(668,153) = HCF(821,668) .

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Frequently Asked Questions on HCF of 821, 668 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 821, 668?

Answer: HCF of 821, 668 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 821, 668 using Euclid's Algorithm?

Answer: For arbitrary numbers 821, 668 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.