Highest Common Factor of 639, 816, 80 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 639, 816, 80 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 639, 816, 80 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 639, 816, 80 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 639, 816, 80 is 1.

HCF(639, 816, 80) = 1

HCF of 639, 816, 80 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 639, 816, 80 is 1.

Highest Common Factor of 639,816,80 using Euclid's algorithm

Highest Common Factor of 639,816,80 is 1

Step 1: Since 816 > 639, we apply the division lemma to 816 and 639, to get

816 = 639 x 1 + 177

Step 2: Since the reminder 639 ≠ 0, we apply division lemma to 177 and 639, to get

639 = 177 x 3 + 108

Step 3: We consider the new divisor 177 and the new remainder 108, and apply the division lemma to get

177 = 108 x 1 + 69

We consider the new divisor 108 and the new remainder 69,and apply the division lemma to get

108 = 69 x 1 + 39

We consider the new divisor 69 and the new remainder 39,and apply the division lemma to get

69 = 39 x 1 + 30

We consider the new divisor 39 and the new remainder 30,and apply the division lemma to get

39 = 30 x 1 + 9

We consider the new divisor 30 and the new remainder 9,and apply the division lemma to get

30 = 9 x 3 + 3

We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get

9 = 3 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 639 and 816 is 3

Notice that 3 = HCF(9,3) = HCF(30,9) = HCF(39,30) = HCF(69,39) = HCF(108,69) = HCF(177,108) = HCF(639,177) = HCF(816,639) .

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

Step 1: Since 80 > 3, we apply the division lemma to 80 and 3, to get

80 = 3 x 26 + 2

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

3 = 2 x 1 + 1

Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 80 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(80,3) .

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Frequently Asked Questions on HCF of 639, 816, 80 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 639, 816, 80?

Answer: HCF of 639, 816, 80 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 639, 816, 80 using Euclid's Algorithm?

Answer: For arbitrary numbers 639, 816, 80 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.