Highest Common Factor of 792, 517, 312 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 792, 517, 312 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 792, 517, 312 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 792, 517, 312 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 792, 517, 312 is 1.

HCF(792, 517, 312) = 1

HCF of 792, 517, 312 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 792, 517, 312 is 1.

Highest Common Factor of 792,517,312 using Euclid's algorithm

Highest Common Factor of 792,517,312 is 1

Step 1: Since 792 > 517, we apply the division lemma to 792 and 517, to get

792 = 517 x 1 + 275

Step 2: Since the reminder 517 ≠ 0, we apply division lemma to 275 and 517, to get

517 = 275 x 1 + 242

Step 3: We consider the new divisor 275 and the new remainder 242, and apply the division lemma to get

275 = 242 x 1 + 33

We consider the new divisor 242 and the new remainder 33,and apply the division lemma to get

242 = 33 x 7 + 11

We consider the new divisor 33 and the new remainder 11,and apply the division lemma to get

33 = 11 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 792 and 517 is 11

Notice that 11 = HCF(33,11) = HCF(242,33) = HCF(275,242) = HCF(517,275) = HCF(792,517) .

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

Step 1: Since 312 > 11, we apply the division lemma to 312 and 11, to get

312 = 11 x 28 + 4

Step 2: Since the reminder 11 ≠ 0, we apply division lemma to 4 and 11, to get

11 = 4 x 2 + 3

Step 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 11 and 312 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(312,11) .

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Frequently Asked Questions on HCF of 792, 517, 312 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 792, 517, 312?

Answer: HCF of 792, 517, 312 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 792, 517, 312 using Euclid's Algorithm?

Answer: For arbitrary numbers 792, 517, 312 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.