Highest Common Factor of 513, 624, 254 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 513, 624, 254 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 513, 624, 254 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 513, 624, 254 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 513, 624, 254 is 1.

HCF(513, 624, 254) = 1

HCF of 513, 624, 254 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 513, 624, 254 is 1.

Highest Common Factor of 513,624,254 using Euclid's algorithm

Highest Common Factor of 513,624,254 is 1

Step 1: Since 624 > 513, we apply the division lemma to 624 and 513, to get

624 = 513 x 1 + 111

Step 2: Since the reminder 513 ≠ 0, we apply division lemma to 111 and 513, to get

513 = 111 x 4 + 69

Step 3: We consider the new divisor 111 and the new remainder 69, and apply the division lemma to get

111 = 69 x 1 + 42

We consider the new divisor 69 and the new remainder 42,and apply the division lemma to get

69 = 42 x 1 + 27

We consider the new divisor 42 and the new remainder 27,and apply the division lemma to get

42 = 27 x 1 + 15

We consider the new divisor 27 and the new remainder 15,and apply the division lemma to get

27 = 15 x 1 + 12

We consider the new divisor 15 and the new remainder 12,and apply the division lemma to get

15 = 12 x 1 + 3

We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get

12 = 3 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 513 and 624 is 3

Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(27,15) = HCF(42,27) = HCF(69,42) = HCF(111,69) = HCF(513,111) = HCF(624,513) .

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

Step 1: Since 254 > 3, we apply the division lemma to 254 and 3, to get

254 = 3 x 84 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma 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 3 and 254 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(254,3) .

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Frequently Asked Questions on HCF of 513, 624, 254 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 513, 624, 254?

Answer: HCF of 513, 624, 254 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 513, 624, 254 using Euclid's Algorithm?

Answer: For arbitrary numbers 513, 624, 254 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.