Highest Common Factor of 916, 527, 912 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 916, 527, 912 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 916, 527, 912 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 916, 527, 912 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 916, 527, 912 is 1.

HCF(916, 527, 912) = 1

HCF of 916, 527, 912 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 916, 527, 912 is 1.

Highest Common Factor of 916,527,912 using Euclid's algorithm

Highest Common Factor of 916,527,912 is 1

Step 1: Since 916 > 527, we apply the division lemma to 916 and 527, to get

916 = 527 x 1 + 389

Step 2: Since the reminder 527 ≠ 0, we apply division lemma to 389 and 527, to get

527 = 389 x 1 + 138

Step 3: We consider the new divisor 389 and the new remainder 138, and apply the division lemma to get

389 = 138 x 2 + 113

We consider the new divisor 138 and the new remainder 113,and apply the division lemma to get

138 = 113 x 1 + 25

We consider the new divisor 113 and the new remainder 25,and apply the division lemma to get

113 = 25 x 4 + 13

We consider the new divisor 25 and the new remainder 13,and apply the division lemma to get

25 = 13 x 1 + 12

We consider the new divisor 13 and the new remainder 12,and apply the division lemma to get

13 = 12 x 1 + 1

We consider the new divisor 12 and the new remainder 1,and apply the division lemma to get

12 = 1 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 916 and 527 is 1

Notice that 1 = HCF(12,1) = HCF(13,12) = HCF(25,13) = HCF(113,25) = HCF(138,113) = HCF(389,138) = HCF(527,389) = HCF(916,527) .

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

Step 1: Since 912 > 1, we apply the division lemma to 912 and 1, to get

912 = 1 x 912 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 912 is 1

Notice that 1 = HCF(912,1) .

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Frequently Asked Questions on HCF of 916, 527, 912 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 916, 527, 912?

Answer: HCF of 916, 527, 912 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 916, 527, 912 using Euclid's Algorithm?

Answer: For arbitrary numbers 916, 527, 912 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.