Highest Common Factor of 565, 408, 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 565, 408, 675 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 565, 408, 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 565, 408, 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 565, 408, 675 is 1.

HCF(565, 408, 675) = 1

HCF of 565, 408, 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 565, 408, 675 is 1.

Highest Common Factor of 565,408,675 using Euclid's algorithm

Highest Common Factor of 565,408,675 is 1

Step 1: Since 565 > 408, we apply the division lemma to 565 and 408, to get

565 = 408 x 1 + 157

Step 2: Since the reminder 408 ≠ 0, we apply division lemma to 157 and 408, to get

408 = 157 x 2 + 94

Step 3: We consider the new divisor 157 and the new remainder 94, and apply the division lemma to get

157 = 94 x 1 + 63

We consider the new divisor 94 and the new remainder 63,and apply the division lemma to get

94 = 63 x 1 + 31

We consider the new divisor 63 and the new remainder 31,and apply the division lemma to get

63 = 31 x 2 + 1

We consider the new divisor 31 and the new remainder 1,and apply the division lemma to get

31 = 1 x 31 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 565 and 408 is 1

Notice that 1 = HCF(31,1) = HCF(63,31) = HCF(94,63) = HCF(157,94) = HCF(408,157) = HCF(565,408) .

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

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

675 = 1 x 675 + 0

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

Notice that 1 = HCF(675,1) .

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Frequently Asked Questions on HCF of 565, 408, 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 565, 408, 675?

Answer: HCF of 565, 408, 675 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 565, 408, 675 using Euclid's Algorithm?

Answer: For arbitrary numbers 565, 408, 675 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.