Highest Common Factor of 718, 278, 569 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 718, 278, 569 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 718, 278, 569 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 718, 278, 569 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 718, 278, 569 is 1.

HCF(718, 278, 569) = 1

HCF of 718, 278, 569 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 718, 278, 569 is 1.

Highest Common Factor of 718,278,569 using Euclid's algorithm

Highest Common Factor of 718,278,569 is 1

Step 1: Since 718 > 278, we apply the division lemma to 718 and 278, to get

718 = 278 x 2 + 162

Step 2: Since the reminder 278 ≠ 0, we apply division lemma to 162 and 278, to get

278 = 162 x 1 + 116

Step 3: We consider the new divisor 162 and the new remainder 116, and apply the division lemma to get

162 = 116 x 1 + 46

We consider the new divisor 116 and the new remainder 46,and apply the division lemma to get

116 = 46 x 2 + 24

We consider the new divisor 46 and the new remainder 24,and apply the division lemma to get

46 = 24 x 1 + 22

We consider the new divisor 24 and the new remainder 22,and apply the division lemma to get

24 = 22 x 1 + 2

We consider the new divisor 22 and the new remainder 2,and apply the division lemma to get

22 = 2 x 11 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 718 and 278 is 2

Notice that 2 = HCF(22,2) = HCF(24,22) = HCF(46,24) = HCF(116,46) = HCF(162,116) = HCF(278,162) = HCF(718,278) .

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

Step 1: Since 569 > 2, we apply the division lemma to 569 and 2, to get

569 = 2 x 284 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 569 is 1

Notice that 1 = HCF(2,1) = HCF(569,2) .

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Frequently Asked Questions on HCF of 718, 278, 569 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 718, 278, 569?

Answer: HCF of 718, 278, 569 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 718, 278, 569 using Euclid's Algorithm?

Answer: For arbitrary numbers 718, 278, 569 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.