Highest Common Factor of 408, 674, 284 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 408, 674, 284 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 408, 674, 284 is 2 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 408, 674, 284 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 408, 674, 284 is 2.

HCF(408, 674, 284) = 2

HCF of 408, 674, 284 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 408, 674, 284 is 2.

Highest Common Factor of 408,674,284 using Euclid's algorithm

Highest Common Factor of 408,674,284 is 2

Step 1: Since 674 > 408, we apply the division lemma to 674 and 408, to get

674 = 408 x 1 + 266

Step 2: Since the reminder 408 ≠ 0, we apply division lemma to 266 and 408, to get

408 = 266 x 1 + 142

Step 3: We consider the new divisor 266 and the new remainder 142, and apply the division lemma to get

266 = 142 x 1 + 124

We consider the new divisor 142 and the new remainder 124,and apply the division lemma to get

142 = 124 x 1 + 18

We consider the new divisor 124 and the new remainder 18,and apply the division lemma to get

124 = 18 x 6 + 16

We consider the new divisor 18 and the new remainder 16,and apply the division lemma to get

18 = 16 x 1 + 2

We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get

16 = 2 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 408 and 674 is 2

Notice that 2 = HCF(16,2) = HCF(18,16) = HCF(124,18) = HCF(142,124) = HCF(266,142) = HCF(408,266) = HCF(674,408) .

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

Step 1: Since 284 > 2, we apply the division lemma to 284 and 2, to get

284 = 2 x 142 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 284 is 2

Notice that 2 = HCF(284,2) .

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Frequently Asked Questions on HCF of 408, 674, 284 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 408, 674, 284?

Answer: HCF of 408, 674, 284 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 408, 674, 284 using Euclid's Algorithm?

Answer: For arbitrary numbers 408, 674, 284 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.