Highest Common Factor of 364, 470, 565 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 364, 470, 565 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 364, 470, 565 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 364, 470, 565 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 364, 470, 565 is 1.

HCF(364, 470, 565) = 1

HCF of 364, 470, 565 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 364, 470, 565 is 1.

Highest Common Factor of 364,470,565 using Euclid's algorithm

Highest Common Factor of 364,470,565 is 1

Step 1: Since 470 > 364, we apply the division lemma to 470 and 364, to get

470 = 364 x 1 + 106

Step 2: Since the reminder 364 ≠ 0, we apply division lemma to 106 and 364, to get

364 = 106 x 3 + 46

Step 3: We consider the new divisor 106 and the new remainder 46, and apply the division lemma to get

106 = 46 x 2 + 14

We consider the new divisor 46 and the new remainder 14,and apply the division lemma to get

46 = 14 x 3 + 4

We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get

14 = 4 x 3 + 2

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 364 and 470 is 2

Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(46,14) = HCF(106,46) = HCF(364,106) = HCF(470,364) .

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

Step 1: Since 565 > 2, we apply the division lemma to 565 and 2, to get

565 = 2 x 282 + 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 565 is 1

Notice that 1 = HCF(2,1) = HCF(565,2) .

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Frequently Asked Questions on HCF of 364, 470, 565 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 364, 470, 565?

Answer: HCF of 364, 470, 565 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 364, 470, 565 using Euclid's Algorithm?

Answer: For arbitrary numbers 364, 470, 565 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.