Highest Common Factor of 421, 959, 60 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, 959, 60 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 421, 959, 60 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, 959, 60 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, 959, 60 is 1.

HCF(421, 959, 60) = 1

HCF of 421, 959, 60 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, 959, 60 is 1.

Highest Common Factor of 421,959,60 using Euclid's algorithm

Highest Common Factor of 421,959,60 is 1

Step 1: Since 959 > 421, we apply the division lemma to 959 and 421, to get

959 = 421 x 2 + 117

Step 2: Since the reminder 421 ≠ 0, we apply division lemma to 117 and 421, to get

421 = 117 x 3 + 70

Step 3: We consider the new divisor 117 and the new remainder 70, and apply the division lemma to get

117 = 70 x 1 + 47

We consider the new divisor 70 and the new remainder 47,and apply the division lemma to get

70 = 47 x 1 + 23

We consider the new divisor 47 and the new remainder 23,and apply the division lemma to get

47 = 23 x 2 + 1

We consider the new divisor 23 and the new remainder 1,and apply the division lemma to get

23 = 1 x 23 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 421 and 959 is 1

Notice that 1 = HCF(23,1) = HCF(47,23) = HCF(70,47) = HCF(117,70) = HCF(421,117) = HCF(959,421) .

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

Step 1: Since 60 > 1, we apply the division lemma to 60 and 1, to get

60 = 1 x 60 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 60 is 1

Notice that 1 = HCF(60,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 421, 959, 60 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, 959, 60?

Answer: HCF of 421, 959, 60 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 421, 959, 60 using Euclid's Algorithm?

Answer: For arbitrary numbers 421, 959, 60 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.