Highest Common Factor of 450, 10631 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 450, 10631 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 450, 10631 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 450, 10631 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 450, 10631 is 1.

HCF(450, 10631) = 1

HCF of 450, 10631 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 450, 10631 is 1.

Highest Common Factor of 450,10631 using Euclid's algorithm

Highest Common Factor of 450,10631 is 1

Step 1: Since 10631 > 450, we apply the division lemma to 10631 and 450, to get

10631 = 450 x 23 + 281

Step 2: Since the reminder 450 ≠ 0, we apply division lemma to 281 and 450, to get

450 = 281 x 1 + 169

Step 3: We consider the new divisor 281 and the new remainder 169, and apply the division lemma to get

281 = 169 x 1 + 112

We consider the new divisor 169 and the new remainder 112,and apply the division lemma to get

169 = 112 x 1 + 57

We consider the new divisor 112 and the new remainder 57,and apply the division lemma to get

112 = 57 x 1 + 55

We consider the new divisor 57 and the new remainder 55,and apply the division lemma to get

57 = 55 x 1 + 2

We consider the new divisor 55 and the new remainder 2,and apply the division lemma to get

55 = 2 x 27 + 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 450 and 10631 is 1

Notice that 1 = HCF(2,1) = HCF(55,2) = HCF(57,55) = HCF(112,57) = HCF(169,112) = HCF(281,169) = HCF(450,281) = HCF(10631,450) .

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Frequently Asked Questions on HCF of 450, 10631 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 450, 10631?

Answer: HCF of 450, 10631 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 450, 10631 using Euclid's Algorithm?

Answer: For arbitrary numbers 450, 10631 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.