Highest Common Factor of 255, 608, 24, 724 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 255, 608, 24, 724 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 255, 608, 24, 724 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 255, 608, 24, 724 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 255, 608, 24, 724 is 1.

HCF(255, 608, 24, 724) = 1

HCF of 255, 608, 24, 724 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 255, 608, 24, 724 is 1.

Highest Common Factor of 255,608,24,724 using Euclid's algorithm

Highest Common Factor of 255,608,24,724 is 1

Step 1: Since 608 > 255, we apply the division lemma to 608 and 255, to get

608 = 255 x 2 + 98

Step 2: Since the reminder 255 ≠ 0, we apply division lemma to 98 and 255, to get

255 = 98 x 2 + 59

Step 3: We consider the new divisor 98 and the new remainder 59, and apply the division lemma to get

98 = 59 x 1 + 39

We consider the new divisor 59 and the new remainder 39,and apply the division lemma to get

59 = 39 x 1 + 20

We consider the new divisor 39 and the new remainder 20,and apply the division lemma to get

39 = 20 x 1 + 19

We consider the new divisor 20 and the new remainder 19,and apply the division lemma to get

20 = 19 x 1 + 1

We consider the new divisor 19 and the new remainder 1,and apply the division lemma to get

19 = 1 x 19 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 255 and 608 is 1

Notice that 1 = HCF(19,1) = HCF(20,19) = HCF(39,20) = HCF(59,39) = HCF(98,59) = HCF(255,98) = HCF(608,255) .

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

Step 1: Since 24 > 1, we apply the division lemma to 24 and 1, to get

24 = 1 x 24 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 24 is 1

Notice that 1 = HCF(24,1) .

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

Step 1: Since 724 > 1, we apply the division lemma to 724 and 1, to get

724 = 1 x 724 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 724 is 1

Notice that 1 = HCF(724,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 255, 608, 24, 724 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 255, 608, 24, 724?

Answer: HCF of 255, 608, 24, 724 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 255, 608, 24, 724 using Euclid's Algorithm?

Answer: For arbitrary numbers 255, 608, 24, 724 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.