Highest Common Factor of 537, 648 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 537, 648 i.e. 3 the largest integer that leaves a remainder zero for all numbers.

HCF of 537, 648 is 3 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 537, 648 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 537, 648 is 3.

HCF(537, 648) = 3

HCF of 537, 648 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 537, 648 is 3.

Highest Common Factor of 537,648 using Euclid's algorithm

Highest Common Factor of 537,648 is 3

Step 1: Since 648 > 537, we apply the division lemma to 648 and 537, to get

648 = 537 x 1 + 111

Step 2: Since the reminder 537 ≠ 0, we apply division lemma to 111 and 537, to get

537 = 111 x 4 + 93

Step 3: We consider the new divisor 111 and the new remainder 93, and apply the division lemma to get

111 = 93 x 1 + 18

We consider the new divisor 93 and the new remainder 18,and apply the division lemma to get

93 = 18 x 5 + 3

We consider the new divisor 18 and the new remainder 3,and apply the division lemma to get

18 = 3 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 537 and 648 is 3

Notice that 3 = HCF(18,3) = HCF(93,18) = HCF(111,93) = HCF(537,111) = HCF(648,537) .

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Frequently Asked Questions on HCF of 537, 648 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 537, 648?

Answer: HCF of 537, 648 is 3 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 537, 648 using Euclid's Algorithm?

Answer: For arbitrary numbers 537, 648 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.