Highest Common Factor of 640, 403, 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 640, 403, 136 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 640, 403, 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 640, 403, 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 640, 403, 136 is 1.

HCF(640, 403, 136) = 1

HCF of 640, 403, 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 640, 403, 136 is 1.

Highest Common Factor of 640,403,136 using Euclid's algorithm

Highest Common Factor of 640,403,136 is 1

Step 1: Since 640 > 403, we apply the division lemma to 640 and 403, to get

640 = 403 x 1 + 237

Step 2: Since the reminder 403 ≠ 0, we apply division lemma to 237 and 403, to get

403 = 237 x 1 + 166

Step 3: We consider the new divisor 237 and the new remainder 166, and apply the division lemma to get

237 = 166 x 1 + 71

We consider the new divisor 166 and the new remainder 71,and apply the division lemma to get

166 = 71 x 2 + 24

We consider the new divisor 71 and the new remainder 24,and apply the division lemma to get

71 = 24 x 2 + 23

We consider the new divisor 24 and the new remainder 23,and apply the division lemma to get

24 = 23 x 1 + 1

We consider the new divisor 23 and the new remainder 1,and apply the division lemma to get

23 = 1 x 23 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 640 and 403 is 1

Notice that 1 = HCF(23,1) = HCF(24,23) = HCF(71,24) = HCF(166,71) = HCF(237,166) = HCF(403,237) = HCF(640,403) .

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 640, 403, 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 640, 403, 136?

Answer: HCF of 640, 403, 136 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 640, 403, 136 using Euclid's Algorithm?

Answer: For arbitrary numbers 640, 403, 136 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.