# Highest Common Factor of 51, 90 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 51, 90 i.e. 3 the largest integer that leaves a remainder zero for all numbers.

HCF of 51, 90 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 51, 90 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 51, 90 is 3.

HCF(51, 90) = 3

## HCF of 51, 90 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 51, 90 is 3. ### Highest Common Factor of 51,90 is 3

Step 1: Since 90 > 51, we apply the division lemma to 90 and 51, to get

90 = 51 x 1 + 39

Step 2: Since the reminder 51 ≠ 0, we apply division lemma to 39 and 51, to get

51 = 39 x 1 + 12

Step 3: We consider the new divisor 39 and the new remainder 12, and apply the division lemma to get

39 = 12 x 3 + 3

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

12 = 3 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 51 and 90 is 3

Notice that 3 = HCF(12,3) = HCF(39,12) = HCF(51,39) = HCF(90,51) .

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### Frequently Asked Questions on HCF of 51, 90 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 51, 90?

Answer: HCF of 51, 90 is 3 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 51, 90 using Euclid's Algorithm?

Answer: For arbitrary numbers 51, 90 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.