Highest Common Factor of 782, 9951 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 782, 9951 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 782, 9951 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 782, 9951 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 782, 9951 is 1.

HCF(782, 9951) = 1

HCF of 782, 9951 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 782, 9951 is 1.

Highest Common Factor of 782,9951 using Euclid's algorithm

Highest Common Factor of 782,9951 is 1

Step 1: Since 9951 > 782, we apply the division lemma to 9951 and 782, to get

9951 = 782 x 12 + 567

Step 2: Since the reminder 782 ≠ 0, we apply division lemma to 567 and 782, to get

782 = 567 x 1 + 215

Step 3: We consider the new divisor 567 and the new remainder 215, and apply the division lemma to get

567 = 215 x 2 + 137

We consider the new divisor 215 and the new remainder 137,and apply the division lemma to get

215 = 137 x 1 + 78

We consider the new divisor 137 and the new remainder 78,and apply the division lemma to get

137 = 78 x 1 + 59

We consider the new divisor 78 and the new remainder 59,and apply the division lemma to get

78 = 59 x 1 + 19

We consider the new divisor 59 and the new remainder 19,and apply the division lemma to get

59 = 19 x 3 + 2

We consider the new divisor 19 and the new remainder 2,and apply the division lemma to get

19 = 2 x 9 + 1

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 782 and 9951 is 1

Notice that 1 = HCF(2,1) = HCF(19,2) = HCF(59,19) = HCF(78,59) = HCF(137,78) = HCF(215,137) = HCF(567,215) = HCF(782,567) = HCF(9951,782) .

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Frequently Asked Questions on HCF of 782, 9951 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 782, 9951?

Answer: HCF of 782, 9951 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 782, 9951 using Euclid's Algorithm?

Answer: For arbitrary numbers 782, 9951 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.