Highest Common Factor of 261, 412, 358 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 261, 412, 358 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 261, 412, 358 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 261, 412, 358 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 261, 412, 358 is 1.

HCF(261, 412, 358) = 1

HCF of 261, 412, 358 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 261, 412, 358 is 1.

Highest Common Factor of 261,412,358 using Euclid's algorithm

Highest Common Factor of 261,412,358 is 1

Step 1: Since 412 > 261, we apply the division lemma to 412 and 261, to get

412 = 261 x 1 + 151

Step 2: Since the reminder 261 ≠ 0, we apply division lemma to 151 and 261, to get

261 = 151 x 1 + 110

Step 3: We consider the new divisor 151 and the new remainder 110, and apply the division lemma to get

151 = 110 x 1 + 41

We consider the new divisor 110 and the new remainder 41,and apply the division lemma to get

110 = 41 x 2 + 28

We consider the new divisor 41 and the new remainder 28,and apply the division lemma to get

41 = 28 x 1 + 13

We consider the new divisor 28 and the new remainder 13,and apply the division lemma to get

28 = 13 x 2 + 2

We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get

13 = 2 x 6 + 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 261 and 412 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(28,13) = HCF(41,28) = HCF(110,41) = HCF(151,110) = HCF(261,151) = HCF(412,261) .

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

Step 1: Since 358 > 1, we apply the division lemma to 358 and 1, to get

358 = 1 x 358 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 358 is 1

Notice that 1 = HCF(358,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 261, 412, 358 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 261, 412, 358?

Answer: HCF of 261, 412, 358 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 261, 412, 358 using Euclid's Algorithm?

Answer: For arbitrary numbers 261, 412, 358 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.