Highest Common Factor of 757, 854, 421 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 757, 854, 421 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 757, 854, 421 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 757, 854, 421 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 757, 854, 421 is 1.

HCF(757, 854, 421) = 1

HCF of 757, 854, 421 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 757, 854, 421 is 1.

Highest Common Factor of 757,854,421 using Euclid's algorithm

Highest Common Factor of 757,854,421 is 1

Step 1: Since 854 > 757, we apply the division lemma to 854 and 757, to get

854 = 757 x 1 + 97

Step 2: Since the reminder 757 ≠ 0, we apply division lemma to 97 and 757, to get

757 = 97 x 7 + 78

Step 3: We consider the new divisor 97 and the new remainder 78, and apply the division lemma to get

97 = 78 x 1 + 19

We consider the new divisor 78 and the new remainder 19,and apply the division lemma to get

78 = 19 x 4 + 2

We consider the new divisor 19 and the new remainder 2,and apply the division lemma to get

19 = 2 x 9 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 757 and 854 is 1

Notice that 1 = HCF(2,1) = HCF(19,2) = HCF(78,19) = HCF(97,78) = HCF(757,97) = HCF(854,757) .

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

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

421 = 1 x 421 + 0

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

Notice that 1 = HCF(421,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 757, 854, 421 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 757, 854, 421?

Answer: HCF of 757, 854, 421 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 757, 854, 421 using Euclid's Algorithm?

Answer: For arbitrary numbers 757, 854, 421 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.