Highest Common Factor of 914, 512, 979 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 914, 512, 979 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 914, 512, 979 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 914, 512, 979 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 914, 512, 979 is 1.

HCF(914, 512, 979) = 1

HCF of 914, 512, 979 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 914, 512, 979 is 1.

Highest Common Factor of 914,512,979 using Euclid's algorithm

Highest Common Factor of 914,512,979 is 1

Step 1: Since 914 > 512, we apply the division lemma to 914 and 512, to get

914 = 512 x 1 + 402

Step 2: Since the reminder 512 ≠ 0, we apply division lemma to 402 and 512, to get

512 = 402 x 1 + 110

Step 3: We consider the new divisor 402 and the new remainder 110, and apply the division lemma to get

402 = 110 x 3 + 72

We consider the new divisor 110 and the new remainder 72,and apply the division lemma to get

110 = 72 x 1 + 38

We consider the new divisor 72 and the new remainder 38,and apply the division lemma to get

72 = 38 x 1 + 34

We consider the new divisor 38 and the new remainder 34,and apply the division lemma to get

38 = 34 x 1 + 4

We consider the new divisor 34 and the new remainder 4,and apply the division lemma to get

34 = 4 x 8 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 914 and 512 is 2

Notice that 2 = HCF(4,2) = HCF(34,4) = HCF(38,34) = HCF(72,38) = HCF(110,72) = HCF(402,110) = HCF(512,402) = HCF(914,512) .

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

Step 1: Since 979 > 2, we apply the division lemma to 979 and 2, to get

979 = 2 x 489 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 979 is 1

Notice that 1 = HCF(2,1) = HCF(979,2) .

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Frequently Asked Questions on HCF of 914, 512, 979 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 914, 512, 979?

Answer: HCF of 914, 512, 979 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 914, 512, 979 using Euclid's Algorithm?

Answer: For arbitrary numbers 914, 512, 979 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.