Highest Common Factor of 460, 730, 624 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 460, 730, 624 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 460, 730, 624 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 460, 730, 624 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 460, 730, 624 is 2.

HCF(460, 730, 624) = 2

HCF of 460, 730, 624 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 460, 730, 624 is 2.

Highest Common Factor of 460,730,624 using Euclid's algorithm

Highest Common Factor of 460,730,624 is 2

Step 1: Since 730 > 460, we apply the division lemma to 730 and 460, to get

730 = 460 x 1 + 270

Step 2: Since the reminder 460 ≠ 0, we apply division lemma to 270 and 460, to get

460 = 270 x 1 + 190

Step 3: We consider the new divisor 270 and the new remainder 190, and apply the division lemma to get

270 = 190 x 1 + 80

We consider the new divisor 190 and the new remainder 80,and apply the division lemma to get

190 = 80 x 2 + 30

We consider the new divisor 80 and the new remainder 30,and apply the division lemma to get

80 = 30 x 2 + 20

We consider the new divisor 30 and the new remainder 20,and apply the division lemma to get

30 = 20 x 1 + 10

We consider the new divisor 20 and the new remainder 10,and apply the division lemma to get

20 = 10 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 460 and 730 is 10

Notice that 10 = HCF(20,10) = HCF(30,20) = HCF(80,30) = HCF(190,80) = HCF(270,190) = HCF(460,270) = HCF(730,460) .


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

Step 1: Since 624 > 10, we apply the division lemma to 624 and 10, to get

624 = 10 x 62 + 4

Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 4 and 10, to get

10 = 4 x 2 + 2

Step 3: 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 10 and 624 is 2

Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(624,10) .

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Frequently Asked Questions on HCF of 460, 730, 624 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 460, 730, 624?

Answer: HCF of 460, 730, 624 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 460, 730, 624 using Euclid's Algorithm?

Answer: For arbitrary numbers 460, 730, 624 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.