Highest Common Factor of 864, 251, 136 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 864, 251, 136 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 864, 251, 136 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 864, 251, 136 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 864, 251, 136 is 1.

HCF(864, 251, 136) = 1

HCF of 864, 251, 136 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 864, 251, 136 is 1.

Highest Common Factor of 864,251,136 using Euclid's algorithm

Highest Common Factor of 864,251,136 is 1

Step 1: Since 864 > 251, we apply the division lemma to 864 and 251, to get

864 = 251 x 3 + 111

Step 2: Since the reminder 251 ≠ 0, we apply division lemma to 111 and 251, to get

251 = 111 x 2 + 29

Step 3: We consider the new divisor 111 and the new remainder 29, and apply the division lemma to get

111 = 29 x 3 + 24

We consider the new divisor 29 and the new remainder 24,and apply the division lemma to get

29 = 24 x 1 + 5

We consider the new divisor 24 and the new remainder 5,and apply the division lemma to get

24 = 5 x 4 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 864 and 251 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(24,5) = HCF(29,24) = HCF(111,29) = HCF(251,111) = HCF(864,251) .

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

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

136 = 1 x 136 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 136 is 1

Notice that 1 = HCF(136,1) .

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Frequently Asked Questions on HCF of 864, 251, 136 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 864, 251, 136?

Answer: HCF of 864, 251, 136 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 864, 251, 136 using Euclid's Algorithm?

Answer: For arbitrary numbers 864, 251, 136 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.