Highest Common Factor of 521, 642, 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 521, 642, 921 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 521, 642, 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 521, 642, 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 521, 642, 921 is 1.

HCF(521, 642, 921) = 1

HCF of 521, 642, 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 521, 642, 921 is 1.

Highest Common Factor of 521,642,921 using Euclid's algorithm

Highest Common Factor of 521,642,921 is 1

Step 1: Since 642 > 521, we apply the division lemma to 642 and 521, to get

642 = 521 x 1 + 121

Step 2: Since the reminder 521 ≠ 0, we apply division lemma to 121 and 521, to get

521 = 121 x 4 + 37

Step 3: We consider the new divisor 121 and the new remainder 37, and apply the division lemma to get

121 = 37 x 3 + 10

We consider the new divisor 37 and the new remainder 10,and apply the division lemma to get

37 = 10 x 3 + 7

We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get

10 = 7 x 1 + 3

We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get

7 = 3 x 2 + 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 521 and 642 is 1

Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(37,10) = HCF(121,37) = HCF(521,121) = HCF(642,521) .

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

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

921 = 1 x 921 + 0

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

Notice that 1 = HCF(921,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 521, 642, 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 521, 642, 921?

Answer: HCF of 521, 642, 921 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 521, 642, 921 using Euclid's Algorithm?

Answer: For arbitrary numbers 521, 642, 921 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.