Highest Common Factor of 420, 512, 696 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, 512, 696 i.e. 4 the largest integer that leaves a remainder zero for all numbers.

HCF of 420, 512, 696 is 4 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, 512, 696 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, 512, 696 is 4.

HCF(420, 512, 696) = 4

HCF of 420, 512, 696 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 420, 512, 696 is 4.

Highest Common Factor of 420,512,696 using Euclid's algorithm

Highest Common Factor of 420,512,696 is 4

Step 1: Since 512 > 420, we apply the division lemma to 512 and 420, to get

512 = 420 x 1 + 92

Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 92 and 420, to get

420 = 92 x 4 + 52

Step 3: We consider the new divisor 92 and the new remainder 52, and apply the division lemma to get

92 = 52 x 1 + 40

We consider the new divisor 52 and the new remainder 40,and apply the division lemma to get

52 = 40 x 1 + 12

We consider the new divisor 40 and the new remainder 12,and apply the division lemma to get

40 = 12 x 3 + 4

We consider the new divisor 12 and the new remainder 4,and apply the division lemma to get

12 = 4 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 420 and 512 is 4

Notice that 4 = HCF(12,4) = HCF(40,12) = HCF(52,40) = HCF(92,52) = HCF(420,92) = HCF(512,420) .

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

Step 1: Since 696 > 4, we apply the division lemma to 696 and 4, to get

696 = 4 x 174 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 696 is 4

Notice that 4 = HCF(696,4) .

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Frequently Asked Questions on HCF of 420, 512, 696 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, 512, 696?

Answer: HCF of 420, 512, 696 is 4 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 420, 512, 696 using Euclid's Algorithm?

Answer: For arbitrary numbers 420, 512, 696 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.