Highest Common Factor of 632, 987, 137, 23 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 632, 987, 137, 23 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 632, 987, 137, 23 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 632, 987, 137, 23 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 632, 987, 137, 23 is 1.

HCF(632, 987, 137, 23) = 1

HCF of 632, 987, 137, 23 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 632, 987, 137, 23 is 1.

Highest Common Factor of 632,987,137,23 using Euclid's algorithm

Highest Common Factor of 632,987,137,23 is 1

Step 1: Since 987 > 632, we apply the division lemma to 987 and 632, to get

987 = 632 x 1 + 355

Step 2: Since the reminder 632 ≠ 0, we apply division lemma to 355 and 632, to get

632 = 355 x 1 + 277

Step 3: We consider the new divisor 355 and the new remainder 277, and apply the division lemma to get

355 = 277 x 1 + 78

We consider the new divisor 277 and the new remainder 78,and apply the division lemma to get

277 = 78 x 3 + 43

We consider the new divisor 78 and the new remainder 43,and apply the division lemma to get

78 = 43 x 1 + 35

We consider the new divisor 43 and the new remainder 35,and apply the division lemma to get

43 = 35 x 1 + 8

We consider the new divisor 35 and the new remainder 8,and apply the division lemma to get

35 = 8 x 4 + 3

We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get

8 = 3 x 2 + 2

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

3 = 2 x 1 + 1

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 632 and 987 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(35,8) = HCF(43,35) = HCF(78,43) = HCF(277,78) = HCF(355,277) = HCF(632,355) = HCF(987,632) .

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

Step 1: Since 137 > 1, we apply the division lemma to 137 and 1, to get

137 = 1 x 137 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 137 is 1

Notice that 1 = HCF(137,1) .

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

Step 1: Since 23 > 1, we apply the division lemma to 23 and 1, 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 1 and 23 is 1

Notice that 1 = HCF(23,1) .

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Frequently Asked Questions on HCF of 632, 987, 137, 23 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 632, 987, 137, 23?

Answer: HCF of 632, 987, 137, 23 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 632, 987, 137, 23 using Euclid's Algorithm?

Answer: For arbitrary numbers 632, 987, 137, 23 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.