Highest Common Factor of 645, 474, 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 645, 474, 136 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 645, 474, 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 645, 474, 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 645, 474, 136 is 1.

HCF(645, 474, 136) = 1

HCF of 645, 474, 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 645, 474, 136 is 1.

Highest Common Factor of 645,474,136 using Euclid's algorithm

Highest Common Factor of 645,474,136 is 1

Step 1: Since 645 > 474, we apply the division lemma to 645 and 474, to get

645 = 474 x 1 + 171

Step 2: Since the reminder 474 ≠ 0, we apply division lemma to 171 and 474, to get

474 = 171 x 2 + 132

Step 3: We consider the new divisor 171 and the new remainder 132, and apply the division lemma to get

171 = 132 x 1 + 39

We consider the new divisor 132 and the new remainder 39,and apply the division lemma to get

132 = 39 x 3 + 15

We consider the new divisor 39 and the new remainder 15,and apply the division lemma to get

39 = 15 x 2 + 9

We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get

15 = 9 x 1 + 6

We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get

9 = 6 x 1 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 645 and 474 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(39,15) = HCF(132,39) = HCF(171,132) = HCF(474,171) = HCF(645,474) .

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

Step 1: Since 136 > 3, we apply the division lemma to 136 and 3, to get

136 = 3 x 45 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 136 is 1

Notice that 1 = HCF(3,1) = HCF(136,3) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 645, 474, 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 645, 474, 136?

Answer: HCF of 645, 474, 136 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 645, 474, 136 using Euclid's Algorithm?

Answer: For arbitrary numbers 645, 474, 136 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.