Highest Common Factor of 260, 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 260, 748 i.e. 4 the largest integer that leaves a remainder zero for all numbers.

HCF of 260, 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 260, 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 260, 748 is 4.

HCF(260, 748) = 4

HCF of 260, 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 260, 748 is 4.

Highest Common Factor of 260,748 using Euclid's algorithm

Highest Common Factor of 260,748 is 4

Step 1: Since 748 > 260, we apply the division lemma to 748 and 260, to get

748 = 260 x 2 + 228

Step 2: Since the reminder 260 ≠ 0, we apply division lemma to 228 and 260, to get

260 = 228 x 1 + 32

Step 3: We consider the new divisor 228 and the new remainder 32, and apply the division lemma to get

228 = 32 x 7 + 4

We consider the new divisor 32 and the new remainder 4, and apply the division lemma to get

32 = 4 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 260 and 748 is 4

Notice that 4 = HCF(32,4) = HCF(228,32) = HCF(260,228) = HCF(748,260) .

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Frequently Asked Questions on HCF of 260, 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 260, 748?

Answer: HCF of 260, 748 is 4 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 260, 748 using Euclid's Algorithm?

Answer: For arbitrary numbers 260, 748 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.