Highest Common Factor of 421, 728, 156 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 421, 728, 156 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 421, 728, 156 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 421, 728, 156 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 421, 728, 156 is 1.

HCF(421, 728, 156) = 1

HCF of 421, 728, 156 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 421, 728, 156 is 1.

Highest Common Factor of 421,728,156 using Euclid's algorithm

Highest Common Factor of 421,728,156 is 1

Step 1: Since 728 > 421, we apply the division lemma to 728 and 421, to get

728 = 421 x 1 + 307

Step 2: Since the reminder 421 ≠ 0, we apply division lemma to 307 and 421, to get

421 = 307 x 1 + 114

Step 3: We consider the new divisor 307 and the new remainder 114, and apply the division lemma to get

307 = 114 x 2 + 79

We consider the new divisor 114 and the new remainder 79,and apply the division lemma to get

114 = 79 x 1 + 35

We consider the new divisor 79 and the new remainder 35,and apply the division lemma to get

79 = 35 x 2 + 9

We consider the new divisor 35 and the new remainder 9,and apply the division lemma to get

35 = 9 x 3 + 8

We consider the new divisor 9 and the new remainder 8,and apply the division lemma to get

9 = 8 x 1 + 1

We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get

8 = 1 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 421 and 728 is 1

Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(35,9) = HCF(79,35) = HCF(114,79) = HCF(307,114) = HCF(421,307) = HCF(728,421) .

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

Step 1: Since 156 > 1, we apply the division lemma to 156 and 1, to get

156 = 1 x 156 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 156 is 1

Notice that 1 = HCF(156,1) .

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Frequently Asked Questions on HCF of 421, 728, 156 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 421, 728, 156?

Answer: HCF of 421, 728, 156 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 421, 728, 156 using Euclid's Algorithm?

Answer: For arbitrary numbers 421, 728, 156 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.