Highest Common Factor of 987, 20513 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 987, 20513 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 987, 20513 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 987, 20513 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 987, 20513 is 1.

HCF(987, 20513) = 1

HCF of 987, 20513 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 987, 20513 is 1.

Highest Common Factor of 987,20513 using Euclid's algorithm

Highest Common Factor of 987,20513 is 1

Step 1: Since 20513 > 987, we apply the division lemma to 20513 and 987, to get

20513 = 987 x 20 + 773

Step 2: Since the reminder 987 ≠ 0, we apply division lemma to 773 and 987, to get

987 = 773 x 1 + 214

Step 3: We consider the new divisor 773 and the new remainder 214, and apply the division lemma to get

773 = 214 x 3 + 131

We consider the new divisor 214 and the new remainder 131,and apply the division lemma to get

214 = 131 x 1 + 83

We consider the new divisor 131 and the new remainder 83,and apply the division lemma to get

131 = 83 x 1 + 48

We consider the new divisor 83 and the new remainder 48,and apply the division lemma to get

83 = 48 x 1 + 35

We consider the new divisor 48 and the new remainder 35,and apply the division lemma to get

48 = 35 x 1 + 13

We consider the new divisor 35 and the new remainder 13,and apply the division lemma to get

35 = 13 x 2 + 9

We consider the new divisor 13 and the new remainder 9,and apply the division lemma to get

13 = 9 x 1 + 4

We consider the new divisor 9 and the new remainder 4,and apply the division lemma to get

9 = 4 x 2 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 987 and 20513 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(13,9) = HCF(35,13) = HCF(48,35) = HCF(83,48) = HCF(131,83) = HCF(214,131) = HCF(773,214) = HCF(987,773) = HCF(20513,987) .

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Frequently Asked Questions on HCF of 987, 20513 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 987, 20513?

Answer: HCF of 987, 20513 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 987, 20513 using Euclid's Algorithm?

Answer: For arbitrary numbers 987, 20513 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.