Highest Common Factor of 648, 135 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 648, 135 i.e. 27 the largest integer that leaves a remainder zero for all numbers.

HCF of 648, 135 is 27 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 648, 135 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 648, 135 is 27.

HCF(648, 135) = 27

HCF of 648, 135 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 648, 135 is 27.

Highest Common Factor of 648,135 using Euclid's algorithm

Highest Common Factor of 648,135 is 27

Step 1: Since 648 > 135, we apply the division lemma to 648 and 135, to get

648 = 135 x 4 + 108

Step 2: Since the reminder 135 ≠ 0, we apply division lemma to 108 and 135, to get

135 = 108 x 1 + 27

Step 3: We consider the new divisor 108 and the new remainder 27, and apply the division lemma to get

108 = 27 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 27, the HCF of 648 and 135 is 27

Notice that 27 = HCF(108,27) = HCF(135,108) = HCF(648,135) .

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Frequently Asked Questions on HCF of 648, 135 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 648, 135?

Answer: HCF of 648, 135 is 27 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 648, 135 using Euclid's Algorithm?

Answer: For arbitrary numbers 648, 135 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.