Highest Common Factor of 258, 136, 453 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 258, 136, 453 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 258, 136, 453 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 258, 136, 453 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 258, 136, 453 is 1.

HCF(258, 136, 453) = 1

HCF of 258, 136, 453 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 258, 136, 453 is 1.

Highest Common Factor of 258,136,453 using Euclid's algorithm

Highest Common Factor of 258,136,453 is 1

Step 1: Since 258 > 136, we apply the division lemma to 258 and 136, to get

258 = 136 x 1 + 122

Step 2: Since the reminder 136 ≠ 0, we apply division lemma to 122 and 136, to get

136 = 122 x 1 + 14

Step 3: We consider the new divisor 122 and the new remainder 14, and apply the division lemma to get

122 = 14 x 8 + 10

We consider the new divisor 14 and the new remainder 10,and apply the division lemma to get

14 = 10 x 1 + 4

We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get

10 = 4 x 2 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 258 and 136 is 2

Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(122,14) = HCF(136,122) = HCF(258,136) .

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

Step 1: Since 453 > 2, we apply the division lemma to 453 and 2, to get

453 = 2 x 226 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 453 is 1

Notice that 1 = HCF(2,1) = HCF(453,2) .

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Frequently Asked Questions on HCF of 258, 136, 453 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 258, 136, 453?

Answer: HCF of 258, 136, 453 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 258, 136, 453 using Euclid's Algorithm?

Answer: For arbitrary numbers 258, 136, 453 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.