Highest Common Factor of 157, 724, 831 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 157, 724, 831 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 157, 724, 831 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 157, 724, 831 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 157, 724, 831 is 1.

HCF(157, 724, 831) = 1

HCF of 157, 724, 831 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 157, 724, 831 is 1.

Highest Common Factor of 157,724,831 using Euclid's algorithm

Highest Common Factor of 157,724,831 is 1

Step 1: Since 724 > 157, we apply the division lemma to 724 and 157, to get

724 = 157 x 4 + 96

Step 2: Since the reminder 157 ≠ 0, we apply division lemma to 96 and 157, to get

157 = 96 x 1 + 61

Step 3: We consider the new divisor 96 and the new remainder 61, and apply the division lemma to get

96 = 61 x 1 + 35

We consider the new divisor 61 and the new remainder 35,and apply the division lemma to get

61 = 35 x 1 + 26

We consider the new divisor 35 and the new remainder 26,and apply the division lemma to get

35 = 26 x 1 + 9

We consider the new divisor 26 and the new remainder 9,and apply the division lemma to get

26 = 9 x 2 + 8

We consider the new divisor 9 and the new remainder 8,and apply the division lemma to get

9 = 8 x 1 + 1

We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get

8 = 1 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 157 and 724 is 1

Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(26,9) = HCF(35,26) = HCF(61,35) = HCF(96,61) = HCF(157,96) = HCF(724,157) .

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

Step 1: Since 831 > 1, we apply the division lemma to 831 and 1, to get

831 = 1 x 831 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 831 is 1

Notice that 1 = HCF(831,1) .

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Frequently Asked Questions on HCF of 157, 724, 831 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 157, 724, 831?

Answer: HCF of 157, 724, 831 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 157, 724, 831 using Euclid's Algorithm?

Answer: For arbitrary numbers 157, 724, 831 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.