Highest Common Factor of 496, 632, 748 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 496, 632, 748 i.e. 4 the largest integer that leaves a remainder zero for all numbers.

HCF of 496, 632, 748 is 4 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 496, 632, 748 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 496, 632, 748 is 4.

HCF(496, 632, 748) = 4

HCF of 496, 632, 748 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 496, 632, 748 is 4.

Highest Common Factor of 496,632,748 using Euclid's algorithm

Highest Common Factor of 496,632,748 is 4

Step 1: Since 632 > 496, we apply the division lemma to 632 and 496, to get

632 = 496 x 1 + 136

Step 2: Since the reminder 496 ≠ 0, we apply division lemma to 136 and 496, to get

496 = 136 x 3 + 88

Step 3: We consider the new divisor 136 and the new remainder 88, and apply the division lemma to get

136 = 88 x 1 + 48

We consider the new divisor 88 and the new remainder 48,and apply the division lemma to get

88 = 48 x 1 + 40

We consider the new divisor 48 and the new remainder 40,and apply the division lemma to get

48 = 40 x 1 + 8

We consider the new divisor 40 and the new remainder 8,and apply the division lemma to get

40 = 8 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 496 and 632 is 8

Notice that 8 = HCF(40,8) = HCF(48,40) = HCF(88,48) = HCF(136,88) = HCF(496,136) = HCF(632,496) .

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

Step 1: Since 748 > 8, we apply the division lemma to 748 and 8, to get

748 = 8 x 93 + 4

Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 4 and 8, to get

8 = 4 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 8 and 748 is 4

Notice that 4 = HCF(8,4) = HCF(748,8) .

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Frequently Asked Questions on HCF of 496, 632, 748 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 496, 632, 748?

Answer: HCF of 496, 632, 748 is 4 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 496, 632, 748 using Euclid's Algorithm?

Answer: For arbitrary numbers 496, 632, 748 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.