Highest Common Factor of 138, 25 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 138, 25 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 138, 25 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 138, 25 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 138, 25 is 1.

HCF(138, 25) = 1

HCF of 138, 25 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 138, 25 is 1.

Highest Common Factor of 138,25 using Euclid's algorithm

Highest Common Factor of 138,25 is 1

Step 1: Since 138 > 25, we apply the division lemma to 138 and 25, to get

138 = 25 x 5 + 13

Step 2: Since the reminder 25 ≠ 0, we apply division lemma to 13 and 25, to get

25 = 13 x 1 + 12

Step 3: We consider the new divisor 13 and the new remainder 12, and apply the division lemma to get

13 = 12 x 1 + 1

We consider the new divisor 12 and the new remainder 1, and apply the division lemma to get

12 = 1 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 138 and 25 is 1

Notice that 1 = HCF(12,1) = HCF(13,12) = HCF(25,13) = HCF(138,25) .

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Frequently Asked Questions on HCF of 138, 25 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 138, 25?

Answer: HCF of 138, 25 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 138, 25 using Euclid's Algorithm?

Answer: For arbitrary numbers 138, 25 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.