Highest Common Factor of 914, 538, 305 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 914, 538, 305 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 914, 538, 305 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 914, 538, 305 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 914, 538, 305 is 1.

HCF(914, 538, 305) = 1

HCF of 914, 538, 305 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 914, 538, 305 is 1.

Highest Common Factor of 914,538,305 using Euclid's algorithm

Highest Common Factor of 914,538,305 is 1

Step 1: Since 914 > 538, we apply the division lemma to 914 and 538, to get

914 = 538 x 1 + 376

Step 2: Since the reminder 538 ≠ 0, we apply division lemma to 376 and 538, to get

538 = 376 x 1 + 162

Step 3: We consider the new divisor 376 and the new remainder 162, and apply the division lemma to get

376 = 162 x 2 + 52

We consider the new divisor 162 and the new remainder 52,and apply the division lemma to get

162 = 52 x 3 + 6

We consider the new divisor 52 and the new remainder 6,and apply the division lemma to get

52 = 6 x 8 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 914 and 538 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(52,6) = HCF(162,52) = HCF(376,162) = HCF(538,376) = HCF(914,538) .

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

Step 1: Since 305 > 2, we apply the division lemma to 305 and 2, to get

305 = 2 x 152 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 305 is 1

Notice that 1 = HCF(2,1) = HCF(305,2) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 914, 538, 305 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 914, 538, 305?

Answer: HCF of 914, 538, 305 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 914, 538, 305 using Euclid's Algorithm?

Answer: For arbitrary numbers 914, 538, 305 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.