Highest Common Factor of 464, 634, 782 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 464, 634, 782 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 464, 634, 782 is 2 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 464, 634, 782 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 464, 634, 782 is 2.

HCF(464, 634, 782) = 2

HCF of 464, 634, 782 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 464, 634, 782 is 2.

Highest Common Factor of 464,634,782 using Euclid's algorithm

Highest Common Factor of 464,634,782 is 2

Step 1: Since 634 > 464, we apply the division lemma to 634 and 464, to get

634 = 464 x 1 + 170

Step 2: Since the reminder 464 ≠ 0, we apply division lemma to 170 and 464, to get

464 = 170 x 2 + 124

Step 3: We consider the new divisor 170 and the new remainder 124, and apply the division lemma to get

170 = 124 x 1 + 46

We consider the new divisor 124 and the new remainder 46,and apply the division lemma to get

124 = 46 x 2 + 32

We consider the new divisor 46 and the new remainder 32,and apply the division lemma to get

46 = 32 x 1 + 14

We consider the new divisor 32 and the new remainder 14,and apply the division lemma to get

32 = 14 x 2 + 4

We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get

14 = 4 x 3 + 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 464 and 634 is 2

Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(32,14) = HCF(46,32) = HCF(124,46) = HCF(170,124) = HCF(464,170) = HCF(634,464) .

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

Step 1: Since 782 > 2, we apply the division lemma to 782 and 2, to get

782 = 2 x 391 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 782 is 2

Notice that 2 = HCF(782,2) .

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Frequently Asked Questions on HCF of 464, 634, 782 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 464, 634, 782?

Answer: HCF of 464, 634, 782 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 464, 634, 782 using Euclid's Algorithm?

Answer: For arbitrary numbers 464, 634, 782 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.