Highest Common Factor of 237, 361, 420 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 237, 361, 420 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 237, 361, 420 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 237, 361, 420 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 237, 361, 420 is 1.

HCF(237, 361, 420) = 1

HCF of 237, 361, 420 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 237, 361, 420 is 1.

Highest Common Factor of 237,361,420 using Euclid's algorithm

Highest Common Factor of 237,361,420 is 1

Step 1: Since 361 > 237, we apply the division lemma to 361 and 237, to get

361 = 237 x 1 + 124

Step 2: Since the reminder 237 ≠ 0, we apply division lemma to 124 and 237, to get

237 = 124 x 1 + 113

Step 3: We consider the new divisor 124 and the new remainder 113, and apply the division lemma to get

124 = 113 x 1 + 11

We consider the new divisor 113 and the new remainder 11,and apply the division lemma to get

113 = 11 x 10 + 3

We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get

11 = 3 x 3 + 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 237 and 361 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(113,11) = HCF(124,113) = HCF(237,124) = HCF(361,237) .

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

Step 1: Since 420 > 1, we apply the division lemma to 420 and 1, to get

420 = 1 x 420 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 420 is 1

Notice that 1 = HCF(420,1) .

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Frequently Asked Questions on HCF of 237, 361, 420 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 237, 361, 420?

Answer: HCF of 237, 361, 420 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 237, 361, 420 using Euclid's Algorithm?

Answer: For arbitrary numbers 237, 361, 420 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.