Highest Common Factor of 420, 39937 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 420, 39937 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 420, 39937 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 420, 39937 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 420, 39937 is 1.

HCF(420, 39937) = 1

HCF of 420, 39937 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 420, 39937 is 1.

Highest Common Factor of 420,39937 using Euclid's algorithm

Highest Common Factor of 420,39937 is 1

Step 1: Since 39937 > 420, we apply the division lemma to 39937 and 420, to get

39937 = 420 x 95 + 37

Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 37 and 420, to get

420 = 37 x 11 + 13

Step 3: We consider the new divisor 37 and the new remainder 13, and apply the division lemma to get

37 = 13 x 2 + 11

We consider the new divisor 13 and the new remainder 11,and apply the division lemma to get

13 = 11 x 1 + 2

We consider the new divisor 11 and the new remainder 2,and apply the division lemma to get

11 = 2 x 5 + 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 420 and 39937 is 1

Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(13,11) = HCF(37,13) = HCF(420,37) = HCF(39937,420) .

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Frequently Asked Questions on HCF of 420, 39937 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 420, 39937?

Answer: HCF of 420, 39937 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 420, 39937 using Euclid's Algorithm?

Answer: For arbitrary numbers 420, 39937 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.