Highest Common Factor of 632, 1121, 8984 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, 1121, 8984 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 632, 1121, 8984 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, 1121, 8984 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, 1121, 8984 is 1.

HCF(632, 1121, 8984) = 1

HCF of 632, 1121, 8984 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, 1121, 8984 is 1.

Highest Common Factor of 632,1121,8984 using Euclid's algorithm

Highest Common Factor of 632,1121,8984 is 1

Step 1: Since 1121 > 632, we apply the division lemma to 1121 and 632, to get

1121 = 632 x 1 + 489

Step 2: Since the reminder 632 ≠ 0, we apply division lemma to 489 and 632, to get

632 = 489 x 1 + 143

Step 3: We consider the new divisor 489 and the new remainder 143, and apply the division lemma to get

489 = 143 x 3 + 60

We consider the new divisor 143 and the new remainder 60,and apply the division lemma to get

143 = 60 x 2 + 23

We consider the new divisor 60 and the new remainder 23,and apply the division lemma to get

60 = 23 x 2 + 14

We consider the new divisor 23 and the new remainder 14,and apply the division lemma to get

23 = 14 x 1 + 9

We consider the new divisor 14 and the new remainder 9,and apply the division lemma to get

14 = 9 x 1 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 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 632 and 1121 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(14,9) = HCF(23,14) = HCF(60,23) = HCF(143,60) = HCF(489,143) = HCF(632,489) = HCF(1121,632) .

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

Step 1: Since 8984 > 1, we apply the division lemma to 8984 and 1, to get

8984 = 1 x 8984 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 8984 is 1

Notice that 1 = HCF(8984,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 632, 1121, 8984 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, 1121, 8984?

Answer: HCF of 632, 1121, 8984 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 632, 1121, 8984 using Euclid's Algorithm?

Answer: For arbitrary numbers 632, 1121, 8984 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.