Highest Common Factor of 280, 220, 416 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 280, 220, 416 i.e. 4 the largest integer that leaves a remainder zero for all numbers.

HCF of 280, 220, 416 is 4 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 280, 220, 416 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 280, 220, 416 is 4.

HCF(280, 220, 416) = 4

HCF of 280, 220, 416 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 280, 220, 416 is 4.

Highest Common Factor of 280,220,416 using Euclid's algorithm

Highest Common Factor of 280,220,416 is 4

Step 1: Since 280 > 220, we apply the division lemma to 280 and 220, to get

280 = 220 x 1 + 60

Step 2: Since the reminder 220 ≠ 0, we apply division lemma to 60 and 220, to get

220 = 60 x 3 + 40

Step 3: We consider the new divisor 60 and the new remainder 40, and apply the division lemma to get

60 = 40 x 1 + 20

We consider the new divisor 40 and the new remainder 20, and apply the division lemma to get

40 = 20 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 280 and 220 is 20

Notice that 20 = HCF(40,20) = HCF(60,40) = HCF(220,60) = HCF(280,220) .

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

Step 1: Since 416 > 20, we apply the division lemma to 416 and 20, to get

416 = 20 x 20 + 16

Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 16 and 20, to get

20 = 16 x 1 + 4

Step 3: We consider the new divisor 16 and the new remainder 4, and apply the division lemma to get

16 = 4 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 20 and 416 is 4

Notice that 4 = HCF(16,4) = HCF(20,16) = HCF(416,20) .

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Frequently Asked Questions on HCF of 280, 220, 416 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 280, 220, 416?

Answer: HCF of 280, 220, 416 is 4 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 280, 220, 416 using Euclid's Algorithm?

Answer: For arbitrary numbers 280, 220, 416 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.