Highest Common Factor of 560, 5970, 8134 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, 5970, 8134 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 560, 5970, 8134 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 560, 5970, 8134 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, 5970, 8134 is 2.

HCF(560, 5970, 8134) = 2

HCF of 560, 5970, 8134 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, 5970, 8134 is 2.

Highest Common Factor of 560,5970,8134 using Euclid's algorithm

Highest Common Factor of 560,5970,8134 is 2

Step 1: Since 5970 > 560, we apply the division lemma to 5970 and 560, to get

5970 = 560 x 10 + 370

Step 2: Since the reminder 560 ≠ 0, we apply division lemma to 370 and 560, to get

560 = 370 x 1 + 190

Step 3: We consider the new divisor 370 and the new remainder 190, and apply the division lemma to get

370 = 190 x 1 + 180

We consider the new divisor 190 and the new remainder 180,and apply the division lemma to get

190 = 180 x 1 + 10

We consider the new divisor 180 and the new remainder 10,and apply the division lemma to get

180 = 10 x 18 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 560 and 5970 is 10

Notice that 10 = HCF(180,10) = HCF(190,180) = HCF(370,190) = HCF(560,370) = HCF(5970,560) .

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

Step 1: Since 8134 > 10, we apply the division lemma to 8134 and 10, to get

8134 = 10 x 813 + 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 8134 is 2

Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(8134,10) .

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Frequently Asked Questions on HCF of 560, 5970, 8134 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, 5970, 8134?

Answer: HCF of 560, 5970, 8134 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 560, 5970, 8134 using Euclid's Algorithm?

Answer: For arbitrary numbers 560, 5970, 8134 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.