Highest Common Factor of 684, 454 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 684, 454 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 684, 454 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 684, 454 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 684, 454 is 2.

HCF(684, 454) = 2

HCF of 684, 454 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 684, 454 is 2.

Highest Common Factor of 684,454 using Euclid's algorithm

Highest Common Factor of 684,454 is 2

Step 1: Since 684 > 454, we apply the division lemma to 684 and 454, to get

684 = 454 x 1 + 230

Step 2: Since the reminder 454 ≠ 0, we apply division lemma to 230 and 454, to get

454 = 230 x 1 + 224

Step 3: We consider the new divisor 230 and the new remainder 224, and apply the division lemma to get

230 = 224 x 1 + 6

We consider the new divisor 224 and the new remainder 6,and apply the division lemma to get

224 = 6 x 37 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 684 and 454 is 2

Notice that 2 = HCF(6,2) = HCF(224,6) = HCF(230,224) = HCF(454,230) = HCF(684,454) .

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Frequently Asked Questions on HCF of 684, 454 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 684, 454?

Answer: HCF of 684, 454 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 684, 454 using Euclid's Algorithm?

Answer: For arbitrary numbers 684, 454 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.