Highest Common Factor of 674, 900, 41 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 674, 900, 41 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 674, 900, 41 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 674, 900, 41 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 674, 900, 41 is 1.

HCF(674, 900, 41) = 1

HCF of 674, 900, 41 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 674, 900, 41 is 1.

Highest Common Factor of 674,900,41 using Euclid's algorithm

Highest Common Factor of 674,900,41 is 1

Step 1: Since 900 > 674, we apply the division lemma to 900 and 674, to get

900 = 674 x 1 + 226

Step 2: Since the reminder 674 ≠ 0, we apply division lemma to 226 and 674, to get

674 = 226 x 2 + 222

Step 3: We consider the new divisor 226 and the new remainder 222, and apply the division lemma to get

226 = 222 x 1 + 4

We consider the new divisor 222 and the new remainder 4,and apply the division lemma to get

222 = 4 x 55 + 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 674 and 900 is 2

Notice that 2 = HCF(4,2) = HCF(222,4) = HCF(226,222) = HCF(674,226) = HCF(900,674) .

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

Step 1: Since 41 > 2, we apply the division lemma to 41 and 2, to get

41 = 2 x 20 + 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 41 is 1

Notice that 1 = HCF(2,1) = HCF(41,2) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 674, 900, 41 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 674, 900, 41?

Answer: HCF of 674, 900, 41 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 674, 900, 41 using Euclid's Algorithm?

Answer: For arbitrary numbers 674, 900, 41 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.