Highest Common Factor of 215, 364, 60 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 215, 364, 60 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 215, 364, 60 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 215, 364, 60 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 215, 364, 60 is 1.

HCF(215, 364, 60) = 1

HCF of 215, 364, 60 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 215, 364, 60 is 1.

Highest Common Factor of 215,364,60 using Euclid's algorithm

Highest Common Factor of 215,364,60 is 1

Step 1: Since 364 > 215, we apply the division lemma to 364 and 215, to get

364 = 215 x 1 + 149

Step 2: Since the reminder 215 ≠ 0, we apply division lemma to 149 and 215, to get

215 = 149 x 1 + 66

Step 3: We consider the new divisor 149 and the new remainder 66, and apply the division lemma to get

149 = 66 x 2 + 17

We consider the new divisor 66 and the new remainder 17,and apply the division lemma to get

66 = 17 x 3 + 15

We consider the new divisor 17 and the new remainder 15,and apply the division lemma to get

17 = 15 x 1 + 2

We consider the new divisor 15 and the new remainder 2,and apply the division lemma to get

15 = 2 x 7 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 215 and 364 is 1

Notice that 1 = HCF(2,1) = HCF(15,2) = HCF(17,15) = HCF(66,17) = HCF(149,66) = HCF(215,149) = HCF(364,215) .

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

Step 1: Since 60 > 1, we apply the division lemma to 60 and 1, to get

60 = 1 x 60 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 60 is 1

Notice that 1 = HCF(60,1) .

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Frequently Asked Questions on HCF of 215, 364, 60 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 215, 364, 60?

Answer: HCF of 215, 364, 60 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 215, 364, 60 using Euclid's Algorithm?

Answer: For arbitrary numbers 215, 364, 60 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.