Highest Common Factor of 195, 108, 640 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 195, 108, 640 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 195, 108, 640 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 195, 108, 640 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 195, 108, 640 is 1.

HCF(195, 108, 640) = 1

HCF of 195, 108, 640 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 195, 108, 640 is 1.

Highest Common Factor of 195,108,640 using Euclid's algorithm

Highest Common Factor of 195,108,640 is 1

Step 1: Since 195 > 108, we apply the division lemma to 195 and 108, to get

195 = 108 x 1 + 87

Step 2: Since the reminder 108 ≠ 0, we apply division lemma to 87 and 108, to get

108 = 87 x 1 + 21

Step 3: We consider the new divisor 87 and the new remainder 21, and apply the division lemma to get

87 = 21 x 4 + 3

We consider the new divisor 21 and the new remainder 3, and apply the division lemma to get

21 = 3 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 195 and 108 is 3

Notice that 3 = HCF(21,3) = HCF(87,21) = HCF(108,87) = HCF(195,108) .


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

Step 1: Since 640 > 3, we apply the division lemma to 640 and 3, to get

640 = 3 x 213 + 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 640 is 1

Notice that 1 = HCF(3,1) = HCF(640,3) .

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Frequently Asked Questions on HCF of 195, 108, 640 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 195, 108, 640?

Answer: HCF of 195, 108, 640 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 195, 108, 640 using Euclid's Algorithm?

Answer: For arbitrary numbers 195, 108, 640 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.