Highest Common Factor of 857, 728, 932 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 857, 728, 932 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 857, 728, 932 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 857, 728, 932 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 857, 728, 932 is 1.

HCF(857, 728, 932) = 1

HCF of 857, 728, 932 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 857, 728, 932 is 1.

Highest Common Factor of 857,728,932 using Euclid's algorithm

Highest Common Factor of 857,728,932 is 1

Step 1: Since 857 > 728, we apply the division lemma to 857 and 728, to get

857 = 728 x 1 + 129

Step 2: Since the reminder 728 ≠ 0, we apply division lemma to 129 and 728, to get

728 = 129 x 5 + 83

Step 3: We consider the new divisor 129 and the new remainder 83, and apply the division lemma to get

129 = 83 x 1 + 46

We consider the new divisor 83 and the new remainder 46,and apply the division lemma to get

83 = 46 x 1 + 37

We consider the new divisor 46 and the new remainder 37,and apply the division lemma to get

46 = 37 x 1 + 9

We consider the new divisor 37 and the new remainder 9,and apply the division lemma to get

37 = 9 x 4 + 1

We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get

9 = 1 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 857 and 728 is 1

Notice that 1 = HCF(9,1) = HCF(37,9) = HCF(46,37) = HCF(83,46) = HCF(129,83) = HCF(728,129) = HCF(857,728) .

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

Step 1: Since 932 > 1, we apply the division lemma to 932 and 1, to get

932 = 1 x 932 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 932 is 1

Notice that 1 = HCF(932,1) .

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Frequently Asked Questions on HCF of 857, 728, 932 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 857, 728, 932?

Answer: HCF of 857, 728, 932 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 857, 728, 932 using Euclid's Algorithm?

Answer: For arbitrary numbers 857, 728, 932 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.