Highest Common Factor of 220, 378, 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 220, 378, 60 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 220, 378, 60 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 220, 378, 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 220, 378, 60 is 2.

HCF(220, 378, 60) = 2

HCF of 220, 378, 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 220, 378, 60 is 2.

Highest Common Factor of 220,378,60 using Euclid's algorithm

Highest Common Factor of 220,378,60 is 2

Step 1: Since 378 > 220, we apply the division lemma to 378 and 220, to get

378 = 220 x 1 + 158

Step 2: Since the reminder 220 ≠ 0, we apply division lemma to 158 and 220, to get

220 = 158 x 1 + 62

Step 3: We consider the new divisor 158 and the new remainder 62, and apply the division lemma to get

158 = 62 x 2 + 34

We consider the new divisor 62 and the new remainder 34,and apply the division lemma to get

62 = 34 x 1 + 28

We consider the new divisor 34 and the new remainder 28,and apply the division lemma to get

34 = 28 x 1 + 6

We consider the new divisor 28 and the new remainder 6,and apply the division lemma to get

28 = 6 x 4 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 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 220 and 378 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(28,6) = HCF(34,28) = HCF(62,34) = HCF(158,62) = HCF(220,158) = HCF(378,220) .

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

Step 1: Since 60 > 2, we apply the division lemma to 60 and 2, to get

60 = 2 x 30 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 60 is 2

Notice that 2 = HCF(60,2) .

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Frequently Asked Questions on HCF of 220, 378, 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 220, 378, 60?

Answer: HCF of 220, 378, 60 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 220, 378, 60 using Euclid's Algorithm?

Answer: For arbitrary numbers 220, 378, 60 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.