Highest Common Factor of 867, 646, 151 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 867, 646, 151 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 867, 646, 151 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 867, 646, 151 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 867, 646, 151 is 1.

HCF(867, 646, 151) = 1

HCF of 867, 646, 151 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 867, 646, 151 is 1.

Highest Common Factor of 867,646,151 using Euclid's algorithm

Highest Common Factor of 867,646,151 is 1

Step 1: Since 867 > 646, we apply the division lemma to 867 and 646, to get

867 = 646 x 1 + 221

Step 2: Since the reminder 646 ≠ 0, we apply division lemma to 221 and 646, to get

646 = 221 x 2 + 204

Step 3: We consider the new divisor 221 and the new remainder 204, and apply the division lemma to get

221 = 204 x 1 + 17

We consider the new divisor 204 and the new remainder 17, and apply the division lemma to get

204 = 17 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 17, the HCF of 867 and 646 is 17

Notice that 17 = HCF(204,17) = HCF(221,204) = HCF(646,221) = HCF(867,646) .

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

Step 1: Since 151 > 17, we apply the division lemma to 151 and 17, to get

151 = 17 x 8 + 15

Step 2: Since the reminder 17 ≠ 0, we apply division lemma to 15 and 17, to get

17 = 15 x 1 + 2

Step 3: We consider the new divisor 15 and the new remainder 2, and apply the division lemma to get

15 = 2 x 7 + 1

We consider the new divisor 2 and the new remainder 1, and apply the division lemma 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 17 and 151 is 1

Notice that 1 = HCF(2,1) = HCF(15,2) = HCF(17,15) = HCF(151,17) .

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Frequently Asked Questions on HCF of 867, 646, 151 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 867, 646, 151?

Answer: HCF of 867, 646, 151 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 867, 646, 151 using Euclid's Algorithm?

Answer: For arbitrary numbers 867, 646, 151 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.