Highest Common Factor of 560, 348, 675 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, 348, 675 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 560, 348, 675 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, 348, 675 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, 348, 675 is 1.

HCF(560, 348, 675) = 1

HCF of 560, 348, 675 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, 348, 675 is 1.

Highest Common Factor of 560,348,675 using Euclid's algorithm

Highest Common Factor of 560,348,675 is 1

Step 1: Since 560 > 348, we apply the division lemma to 560 and 348, to get

560 = 348 x 1 + 212

Step 2: Since the reminder 348 ≠ 0, we apply division lemma to 212 and 348, to get

348 = 212 x 1 + 136

Step 3: We consider the new divisor 212 and the new remainder 136, and apply the division lemma to get

212 = 136 x 1 + 76

We consider the new divisor 136 and the new remainder 76,and apply the division lemma to get

136 = 76 x 1 + 60

We consider the new divisor 76 and the new remainder 60,and apply the division lemma to get

76 = 60 x 1 + 16

We consider the new divisor 60 and the new remainder 16,and apply the division lemma to get

60 = 16 x 3 + 12

We consider the new divisor 16 and the new remainder 12,and apply the division lemma to get

16 = 12 x 1 + 4

We consider the new divisor 12 and the new remainder 4,and apply the division lemma to get

12 = 4 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 560 and 348 is 4

Notice that 4 = HCF(12,4) = HCF(16,12) = HCF(60,16) = HCF(76,60) = HCF(136,76) = HCF(212,136) = HCF(348,212) = HCF(560,348) .

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

Step 1: Since 675 > 4, we apply the division lemma to 675 and 4, to get

675 = 4 x 168 + 3

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get

4 = 3 x 1 + 1

Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 675 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(675,4) .

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Frequently Asked Questions on HCF of 560, 348, 675 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, 348, 675?

Answer: HCF of 560, 348, 675 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 560, 348, 675 using Euclid's Algorithm?

Answer: For arbitrary numbers 560, 348, 675 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.