Highest Common Factor of 974, 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 974, 529 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 974, 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 974, 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 974, 529 is 1.

HCF(974, 529) = 1

HCF of 974, 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 974, 529 is 1.

Highest Common Factor of 974,529 using Euclid's algorithm

Highest Common Factor of 974,529 is 1

Step 1: Since 974 > 529, we apply the division lemma to 974 and 529, to get

974 = 529 x 1 + 445

Step 2: Since the reminder 529 ≠ 0, we apply division lemma to 445 and 529, to get

529 = 445 x 1 + 84

Step 3: We consider the new divisor 445 and the new remainder 84, and apply the division lemma to get

445 = 84 x 5 + 25

We consider the new divisor 84 and the new remainder 25,and apply the division lemma to get

84 = 25 x 3 + 9

We consider the new divisor 25 and the new remainder 9,and apply the division lemma to get

25 = 9 x 2 + 7

We consider the new divisor 9 and the new remainder 7,and apply the division lemma to get

9 = 7 x 1 + 2

We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get

7 = 2 x 3 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 974 and 529 is 1

Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(25,9) = HCF(84,25) = HCF(445,84) = HCF(529,445) = HCF(974,529) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 974, 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 974, 529?

Answer: HCF of 974, 529 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 974, 529 using Euclid's Algorithm?

Answer: For arbitrary numbers 974, 529 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.