Highest Common Factor of 560, 759, 918 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 560, 759, 918 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 560, 759, 918 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 560, 759, 918 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 560, 759, 918 is 1.

HCF(560, 759, 918) = 1

HCF of 560, 759, 918 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 560, 759, 918 is 1.

Highest Common Factor of 560,759,918 using Euclid's algorithm

Highest Common Factor of 560,759,918 is 1

Step 1: Since 759 > 560, we apply the division lemma to 759 and 560, to get

759 = 560 x 1 + 199

Step 2: Since the reminder 560 ≠ 0, we apply division lemma to 199 and 560, to get

560 = 199 x 2 + 162

Step 3: We consider the new divisor 199 and the new remainder 162, and apply the division lemma to get

199 = 162 x 1 + 37

We consider the new divisor 162 and the new remainder 37,and apply the division lemma to get

162 = 37 x 4 + 14

We consider the new divisor 37 and the new remainder 14,and apply the division lemma to get

37 = 14 x 2 + 9

We consider the new divisor 14 and the new remainder 9,and apply the division lemma to get

14 = 9 x 1 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 560 and 759 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(14,9) = HCF(37,14) = HCF(162,37) = HCF(199,162) = HCF(560,199) = HCF(759,560) .

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

Step 1: Since 918 > 1, we apply the division lemma to 918 and 1, to get

918 = 1 x 918 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 918 is 1

Notice that 1 = HCF(918,1) .

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Frequently Asked Questions on HCF of 560, 759, 918 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 560, 759, 918?

Answer: HCF of 560, 759, 918 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 560, 759, 918 using Euclid's Algorithm?

Answer: For arbitrary numbers 560, 759, 918 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.