Highest Common Factor of 121, 450 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 121, 450 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 121, 450 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 121, 450 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 121, 450 is 1.

HCF(121, 450) = 1

HCF of 121, 450 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 121, 450 is 1.

Highest Common Factor of 121,450 using Euclid's algorithm

Highest Common Factor of 121,450 is 1

Step 1: Since 450 > 121, we apply the division lemma to 450 and 121, to get

450 = 121 x 3 + 87

Step 2: Since the reminder 121 ≠ 0, we apply division lemma to 87 and 121, to get

121 = 87 x 1 + 34

Step 3: We consider the new divisor 87 and the new remainder 34, and apply the division lemma to get

87 = 34 x 2 + 19

We consider the new divisor 34 and the new remainder 19,and apply the division lemma to get

34 = 19 x 1 + 15

We consider the new divisor 19 and the new remainder 15,and apply the division lemma to get

19 = 15 x 1 + 4

We consider the new divisor 15 and the new remainder 4,and apply the division lemma to get

15 = 4 x 3 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

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

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 121 and 450 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(15,4) = HCF(19,15) = HCF(34,19) = HCF(87,34) = HCF(121,87) = HCF(450,121) .

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Frequently Asked Questions on HCF of 121, 450 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 121, 450?

Answer: HCF of 121, 450 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 121, 450 using Euclid's Algorithm?

Answer: For arbitrary numbers 121, 450 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.