Highest Common Factor of 685, 931, 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 685, 931, 932 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 685, 931, 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 685, 931, 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 685, 931, 932 is 1.

HCF(685, 931, 932) = 1

HCF of 685, 931, 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 685, 931, 932 is 1.

Highest Common Factor of 685,931,932 using Euclid's algorithm

Highest Common Factor of 685,931,932 is 1

Step 1: Since 931 > 685, we apply the division lemma to 931 and 685, to get

931 = 685 x 1 + 246

Step 2: Since the reminder 685 ≠ 0, we apply division lemma to 246 and 685, to get

685 = 246 x 2 + 193

Step 3: We consider the new divisor 246 and the new remainder 193, and apply the division lemma to get

246 = 193 x 1 + 53

We consider the new divisor 193 and the new remainder 53,and apply the division lemma to get

193 = 53 x 3 + 34

We consider the new divisor 53 and the new remainder 34,and apply the division lemma to get

53 = 34 x 1 + 19

We consider the new divisor 34 and the new remainder 19,and apply the division lemma to get

34 = 19 x 1 + 15

We consider the new divisor 19 and the new remainder 15,and apply the division lemma to get

19 = 15 x 1 + 4

We consider the new divisor 15 and the new remainder 4,and apply the division lemma to get

15 = 4 x 3 + 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 685 and 931 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(15,4) = HCF(19,15) = HCF(34,19) = HCF(53,34) = HCF(193,53) = HCF(246,193) = HCF(685,246) = HCF(931,685) .

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 685, 931, 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 685, 931, 932?

Answer: HCF of 685, 931, 932 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 685, 931, 932 using Euclid's Algorithm?

Answer: For arbitrary numbers 685, 931, 932 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.