Highest Common Factor of 462, 712, 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 462, 712, 921 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 462, 712, 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 462, 712, 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 462, 712, 921 is 1.

HCF(462, 712, 921) = 1

HCF of 462, 712, 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 462, 712, 921 is 1.

Highest Common Factor of 462,712,921 using Euclid's algorithm

Highest Common Factor of 462,712,921 is 1

Step 1: Since 712 > 462, we apply the division lemma to 712 and 462, to get

712 = 462 x 1 + 250

Step 2: Since the reminder 462 ≠ 0, we apply division lemma to 250 and 462, to get

462 = 250 x 1 + 212

Step 3: We consider the new divisor 250 and the new remainder 212, and apply the division lemma to get

250 = 212 x 1 + 38

We consider the new divisor 212 and the new remainder 38,and apply the division lemma to get

212 = 38 x 5 + 22

We consider the new divisor 38 and the new remainder 22,and apply the division lemma to get

38 = 22 x 1 + 16

We consider the new divisor 22 and the new remainder 16,and apply the division lemma to get

22 = 16 x 1 + 6

We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get

16 = 6 x 2 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 462 and 712 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(22,16) = HCF(38,22) = HCF(212,38) = HCF(250,212) = HCF(462,250) = HCF(712,462) .

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

Step 1: Since 921 > 2, we apply the division lemma to 921 and 2, to get

921 = 2 x 460 + 1

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

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 921 is 1

Notice that 1 = HCF(2,1) = HCF(921,2) .

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Frequently Asked Questions on HCF of 462, 712, 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 462, 712, 921?

Answer: HCF of 462, 712, 921 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 462, 712, 921 using Euclid's Algorithm?

Answer: For arbitrary numbers 462, 712, 921 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.