Highest Common Factor of 643, 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 643, 748 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 643, 748 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 643, 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 643, 748 is 1.

HCF(643, 748) = 1

HCF of 643, 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 643, 748 is 1.

Highest Common Factor of 643,748 using Euclid's algorithm

Highest Common Factor of 643,748 is 1

Step 1: Since 748 > 643, we apply the division lemma to 748 and 643, to get

748 = 643 x 1 + 105

Step 2: Since the reminder 643 ≠ 0, we apply division lemma to 105 and 643, to get

643 = 105 x 6 + 13

Step 3: We consider the new divisor 105 and the new remainder 13, and apply the division lemma to get

105 = 13 x 8 + 1

We consider the new divisor 13 and the new remainder 1, and apply the division lemma to get

13 = 1 x 13 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 643 and 748 is 1

Notice that 1 = HCF(13,1) = HCF(105,13) = HCF(643,105) = HCF(748,643) .

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Frequently Asked Questions on HCF of 643, 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 643, 748?

Answer: HCF of 643, 748 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 643, 748 using Euclid's Algorithm?

Answer: For arbitrary numbers 643, 748 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.