Highest Common Factor of 762, 9471, 6224 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 762, 9471, 6224 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 762, 9471, 6224 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 762, 9471, 6224 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 762, 9471, 6224 is 1.

HCF(762, 9471, 6224) = 1

HCF of 762, 9471, 6224 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 762, 9471, 6224 is 1.

Highest Common Factor of 762,9471,6224 using Euclid's algorithm

Highest Common Factor of 762,9471,6224 is 1

Step 1: Since 9471 > 762, we apply the division lemma to 9471 and 762, to get

9471 = 762 x 12 + 327

Step 2: Since the reminder 762 ≠ 0, we apply division lemma to 327 and 762, to get

762 = 327 x 2 + 108

Step 3: We consider the new divisor 327 and the new remainder 108, and apply the division lemma to get

327 = 108 x 3 + 3

We consider the new divisor 108 and the new remainder 3, and apply the division lemma to get

108 = 3 x 36 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 762 and 9471 is 3

Notice that 3 = HCF(108,3) = HCF(327,108) = HCF(762,327) = HCF(9471,762) .

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

Step 1: Since 6224 > 3, we apply the division lemma to 6224 and 3, to get

6224 = 3 x 2074 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma 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 3 and 6224 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(6224,3) .

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Frequently Asked Questions on HCF of 762, 9471, 6224 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 762, 9471, 6224?

Answer: HCF of 762, 9471, 6224 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 762, 9471, 6224 using Euclid's Algorithm?

Answer: For arbitrary numbers 762, 9471, 6224 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.