Highest Common Factor of 640, 441, 129 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, 441, 129 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 640, 441, 129 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, 441, 129 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, 441, 129 is 1.

HCF(640, 441, 129) = 1

HCF of 640, 441, 129 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, 441, 129 is 1.

Highest Common Factor of 640,441,129 using Euclid's algorithm

Highest Common Factor of 640,441,129 is 1

Step 1: Since 640 > 441, we apply the division lemma to 640 and 441, to get

640 = 441 x 1 + 199

Step 2: Since the reminder 441 ≠ 0, we apply division lemma to 199 and 441, to get

441 = 199 x 2 + 43

Step 3: We consider the new divisor 199 and the new remainder 43, and apply the division lemma to get

199 = 43 x 4 + 27

We consider the new divisor 43 and the new remainder 27,and apply the division lemma to get

43 = 27 x 1 + 16

We consider the new divisor 27 and the new remainder 16,and apply the division lemma to get

27 = 16 x 1 + 11

We consider the new divisor 16 and the new remainder 11,and apply the division lemma to get

16 = 11 x 1 + 5

We consider the new divisor 11 and the new remainder 5,and apply the division lemma to get

11 = 5 x 2 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 640 and 441 is 1

Notice that 1 = HCF(5,1) = HCF(11,5) = HCF(16,11) = HCF(27,16) = HCF(43,27) = HCF(199,43) = HCF(441,199) = HCF(640,441) .

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

Step 1: Since 129 > 1, we apply the division lemma to 129 and 1, to get

129 = 1 x 129 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 129 is 1

Notice that 1 = HCF(129,1) .

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Frequently Asked Questions on HCF of 640, 441, 129 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, 441, 129?

Answer: HCF of 640, 441, 129 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 640, 441, 129 using Euclid's Algorithm?

Answer: For arbitrary numbers 640, 441, 129 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.