Highest Common Factor of 84, 728, 412 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 84, 728, 412 i.e. 4 the largest integer that leaves a remainder zero for all numbers.

HCF of 84, 728, 412 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 84, 728, 412 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 84, 728, 412 is 4.

HCF(84, 728, 412) = 4

HCF of 84, 728, 412 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 84, 728, 412 is 4.

Highest Common Factor of 84,728,412 using Euclid's algorithm

Highest Common Factor of 84,728,412 is 4

Step 1: Since 728 > 84, we apply the division lemma to 728 and 84, to get

728 = 84 x 8 + 56

Step 2: Since the reminder 84 ≠ 0, we apply division lemma to 56 and 84, to get

84 = 56 x 1 + 28

Step 3: We consider the new divisor 56 and the new remainder 28, and apply the division lemma to get

56 = 28 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 28, the HCF of 84 and 728 is 28

Notice that 28 = HCF(56,28) = HCF(84,56) = HCF(728,84) .

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

Step 1: Since 412 > 28, we apply the division lemma to 412 and 28, to get

412 = 28 x 14 + 20

Step 2: Since the reminder 28 ≠ 0, we apply division lemma to 20 and 28, to get

28 = 20 x 1 + 8

Step 3: We consider the new divisor 20 and the new remainder 8, and apply the division lemma to get

20 = 8 x 2 + 4

We consider the new divisor 8 and the new remainder 4, and apply the division lemma to get

8 = 4 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 28 and 412 is 4

Notice that 4 = HCF(8,4) = HCF(20,8) = HCF(28,20) = HCF(412,28) .

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Frequently Asked Questions on HCF of 84, 728, 412 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 84, 728, 412?

Answer: HCF of 84, 728, 412 is 4 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 84, 728, 412 using Euclid's Algorithm?

Answer: For arbitrary numbers 84, 728, 412 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.