Highest Common Factor of 504, 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 504, 420 i.e. 84 the largest integer that leaves a remainder zero for all numbers.

HCF of 504, 420 is 84 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 504, 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 504, 420 is 84.

HCF(504, 420) = 84

HCF of 504, 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 504, 420 is 84.

Highest Common Factor of 504,420 using Euclid's algorithm

Highest Common Factor of 504,420 is 84

Step 1: Since 504 > 420, we apply the division lemma to 504 and 420, to get

504 = 420 x 1 + 84

Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 84 and 420, to get

420 = 84 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 84, the HCF of 504 and 420 is 84

Notice that 84 = HCF(420,84) = HCF(504,420) .

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Frequently Asked Questions on HCF of 504, 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 504, 420?

Answer: HCF of 504, 420 is 84 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 504, 420 using Euclid's Algorithm?

Answer: For arbitrary numbers 504, 420 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.