Highest Common Factor of 640, 413, 90 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, 413, 90 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 640, 413, 90 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, 413, 90 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, 413, 90 is 1.

HCF(640, 413, 90) = 1

HCF of 640, 413, 90 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, 413, 90 is 1.

Highest Common Factor of 640,413,90 using Euclid's algorithm

Highest Common Factor of 640,413,90 is 1

Step 1: Since 640 > 413, we apply the division lemma to 640 and 413, to get

640 = 413 x 1 + 227

Step 2: Since the reminder 413 ≠ 0, we apply division lemma to 227 and 413, to get

413 = 227 x 1 + 186

Step 3: We consider the new divisor 227 and the new remainder 186, and apply the division lemma to get

227 = 186 x 1 + 41

We consider the new divisor 186 and the new remainder 41,and apply the division lemma to get

186 = 41 x 4 + 22

We consider the new divisor 41 and the new remainder 22,and apply the division lemma to get

41 = 22 x 1 + 19

We consider the new divisor 22 and the new remainder 19,and apply the division lemma to get

22 = 19 x 1 + 3

We consider the new divisor 19 and the new remainder 3,and apply the division lemma to get

19 = 3 x 6 + 1

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 640 and 413 is 1

Notice that 1 = HCF(3,1) = HCF(19,3) = HCF(22,19) = HCF(41,22) = HCF(186,41) = HCF(227,186) = HCF(413,227) = HCF(640,413) .

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

Step 1: Since 90 > 1, we apply the division lemma to 90 and 1, to get

90 = 1 x 90 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 90 is 1

Notice that 1 = HCF(90,1) .

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Frequently Asked Questions on HCF of 640, 413, 90 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, 413, 90?

Answer: HCF of 640, 413, 90 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 640, 413, 90 using Euclid's Algorithm?

Answer: For arbitrary numbers 640, 413, 90 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.