Highest Common Factor of 636, 872, 167 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 636, 872, 167 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 636, 872, 167 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 636, 872, 167 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 636, 872, 167 is 1.

HCF(636, 872, 167) = 1

HCF of 636, 872, 167 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 636, 872, 167 is 1.

Highest Common Factor of 636,872,167 using Euclid's algorithm

Highest Common Factor of 636,872,167 is 1

Step 1: Since 872 > 636, we apply the division lemma to 872 and 636, to get

872 = 636 x 1 + 236

Step 2: Since the reminder 636 ≠ 0, we apply division lemma to 236 and 636, to get

636 = 236 x 2 + 164

Step 3: We consider the new divisor 236 and the new remainder 164, and apply the division lemma to get

236 = 164 x 1 + 72

We consider the new divisor 164 and the new remainder 72,and apply the division lemma to get

164 = 72 x 2 + 20

We consider the new divisor 72 and the new remainder 20,and apply the division lemma to get

72 = 20 x 3 + 12

We consider the new divisor 20 and the new remainder 12,and apply the division lemma to get

20 = 12 x 1 + 8

We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get

12 = 8 x 1 + 4

We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get

8 = 4 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 636 and 872 is 4

Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(20,12) = HCF(72,20) = HCF(164,72) = HCF(236,164) = HCF(636,236) = HCF(872,636) .

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

Step 1: Since 167 > 4, we apply the division lemma to 167 and 4, to get

167 = 4 x 41 + 3

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get

4 = 3 x 1 + 1

Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 167 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(167,4) .

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Frequently Asked Questions on HCF of 636, 872, 167 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 636, 872, 167?

Answer: HCF of 636, 872, 167 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 636, 872, 167 using Euclid's Algorithm?

Answer: For arbitrary numbers 636, 872, 167 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.