Highest Common Factor of 423, 641, 664 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 423, 641, 664 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 423, 641, 664 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 423, 641, 664 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 423, 641, 664 is 1.

HCF(423, 641, 664) = 1

HCF of 423, 641, 664 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 423, 641, 664 is 1.

Highest Common Factor of 423,641,664 using Euclid's algorithm

Highest Common Factor of 423,641,664 is 1

Step 1: Since 641 > 423, we apply the division lemma to 641 and 423, to get

641 = 423 x 1 + 218

Step 2: Since the reminder 423 ≠ 0, we apply division lemma to 218 and 423, to get

423 = 218 x 1 + 205

Step 3: We consider the new divisor 218 and the new remainder 205, and apply the division lemma to get

218 = 205 x 1 + 13

We consider the new divisor 205 and the new remainder 13,and apply the division lemma to get

205 = 13 x 15 + 10

We consider the new divisor 13 and the new remainder 10,and apply the division lemma to get

13 = 10 x 1 + 3

We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get

10 = 3 x 3 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 423 and 641 is 1

Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(13,10) = HCF(205,13) = HCF(218,205) = HCF(423,218) = HCF(641,423) .

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

Step 1: Since 664 > 1, we apply the division lemma to 664 and 1, to get

664 = 1 x 664 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 664 is 1

Notice that 1 = HCF(664,1) .

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Frequently Asked Questions on HCF of 423, 641, 664 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 423, 641, 664?

Answer: HCF of 423, 641, 664 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 423, 641, 664 using Euclid's Algorithm?

Answer: For arbitrary numbers 423, 641, 664 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.