Highest Common Factor of 679, 840, 921 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 679, 840, 921 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 679, 840, 921 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 679, 840, 921 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 679, 840, 921 is 1.

HCF(679, 840, 921) = 1

HCF of 679, 840, 921 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 679, 840, 921 is 1.

Highest Common Factor of 679,840,921 using Euclid's algorithm

Highest Common Factor of 679,840,921 is 1

Step 1: Since 840 > 679, we apply the division lemma to 840 and 679, to get

840 = 679 x 1 + 161

Step 2: Since the reminder 679 ≠ 0, we apply division lemma to 161 and 679, to get

679 = 161 x 4 + 35

Step 3: We consider the new divisor 161 and the new remainder 35, and apply the division lemma to get

161 = 35 x 4 + 21

We consider the new divisor 35 and the new remainder 21,and apply the division lemma to get

35 = 21 x 1 + 14

We consider the new divisor 21 and the new remainder 14,and apply the division lemma to get

21 = 14 x 1 + 7

We consider the new divisor 14 and the new remainder 7,and apply the division lemma to get

14 = 7 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 679 and 840 is 7

Notice that 7 = HCF(14,7) = HCF(21,14) = HCF(35,21) = HCF(161,35) = HCF(679,161) = HCF(840,679) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 921 > 7, we apply the division lemma to 921 and 7, to get

921 = 7 x 131 + 4

Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 4 and 7, to get

7 = 4 x 1 + 3

Step 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 7 and 921 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(921,7) .

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Frequently Asked Questions on HCF of 679, 840, 921 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 679, 840, 921?

Answer: HCF of 679, 840, 921 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 679, 840, 921 using Euclid's Algorithm?

Answer: For arbitrary numbers 679, 840, 921 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.