Highest Common Factor of 254, 451, 60 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 254, 451, 60 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 254, 451, 60 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 254, 451, 60 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 254, 451, 60 is 1.

HCF(254, 451, 60) = 1

HCF of 254, 451, 60 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 254, 451, 60 is 1.

Highest Common Factor of 254,451,60 using Euclid's algorithm

Highest Common Factor of 254,451,60 is 1

Step 1: Since 451 > 254, we apply the division lemma to 451 and 254, to get

451 = 254 x 1 + 197

Step 2: Since the reminder 254 ≠ 0, we apply division lemma to 197 and 254, to get

254 = 197 x 1 + 57

Step 3: We consider the new divisor 197 and the new remainder 57, and apply the division lemma to get

197 = 57 x 3 + 26

We consider the new divisor 57 and the new remainder 26,and apply the division lemma to get

57 = 26 x 2 + 5

We consider the new divisor 26 and the new remainder 5,and apply the division lemma to get

26 = 5 x 5 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 254 and 451 is 1

Notice that 1 = HCF(5,1) = HCF(26,5) = HCF(57,26) = HCF(197,57) = HCF(254,197) = HCF(451,254) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 60 > 1, we apply the division lemma to 60 and 1, to get

60 = 1 x 60 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 60 is 1

Notice that 1 = HCF(60,1) .

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Frequently Asked Questions on HCF of 254, 451, 60 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 254, 451, 60?

Answer: HCF of 254, 451, 60 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 254, 451, 60 using Euclid's Algorithm?

Answer: For arbitrary numbers 254, 451, 60 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.