Highest Common Factor of 921, 529 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 921, 529 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 921, 529 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 921, 529 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 921, 529 is 1.

HCF(921, 529) = 1

HCF of 921, 529 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 921, 529 is 1.

Highest Common Factor of 921,529 using Euclid's algorithm

Highest Common Factor of 921,529 is 1

Step 1: Since 921 > 529, we apply the division lemma to 921 and 529, to get

921 = 529 x 1 + 392

Step 2: Since the reminder 529 ≠ 0, we apply division lemma to 392 and 529, to get

529 = 392 x 1 + 137

Step 3: We consider the new divisor 392 and the new remainder 137, and apply the division lemma to get

392 = 137 x 2 + 118

We consider the new divisor 137 and the new remainder 118,and apply the division lemma to get

137 = 118 x 1 + 19

We consider the new divisor 118 and the new remainder 19,and apply the division lemma to get

118 = 19 x 6 + 4

We consider the new divisor 19 and the new remainder 4,and apply the division lemma to get

19 = 4 x 4 + 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 921 and 529 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(19,4) = HCF(118,19) = HCF(137,118) = HCF(392,137) = HCF(529,392) = HCF(921,529) .

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Frequently Asked Questions on HCF of 921, 529 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 921, 529?

Answer: HCF of 921, 529 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 921, 529 using Euclid's Algorithm?

Answer: For arbitrary numbers 921, 529 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.