Highest Common Factor of 924, 731 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 924, 731 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 924, 731 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 924, 731 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 924, 731 is 1.

HCF(924, 731) = 1

HCF of 924, 731 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 924, 731 is 1.

Highest Common Factor of 924,731 using Euclid's algorithm

Highest Common Factor of 924,731 is 1

Step 1: Since 924 > 731, we apply the division lemma to 924 and 731, to get

924 = 731 x 1 + 193

Step 2: Since the reminder 731 ≠ 0, we apply division lemma to 193 and 731, to get

731 = 193 x 3 + 152

Step 3: We consider the new divisor 193 and the new remainder 152, and apply the division lemma to get

193 = 152 x 1 + 41

We consider the new divisor 152 and the new remainder 41,and apply the division lemma to get

152 = 41 x 3 + 29

We consider the new divisor 41 and the new remainder 29,and apply the division lemma to get

41 = 29 x 1 + 12

We consider the new divisor 29 and the new remainder 12,and apply the division lemma to get

29 = 12 x 2 + 5

We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get

12 = 5 x 2 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 924 and 731 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(29,12) = HCF(41,29) = HCF(152,41) = HCF(193,152) = HCF(731,193) = HCF(924,731) .

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Frequently Asked Questions on HCF of 924, 731 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 924, 731?

Answer: HCF of 924, 731 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 924, 731 using Euclid's Algorithm?

Answer: For arbitrary numbers 924, 731 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.