Highest Common Factor of 89, 657, 160, 220 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 89, 657, 160, 220 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 89, 657, 160, 220 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 89, 657, 160, 220 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 89, 657, 160, 220 is 1.

HCF(89, 657, 160, 220) = 1

HCF of 89, 657, 160, 220 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 89, 657, 160, 220 is 1.

Highest Common Factor of 89,657,160,220 using Euclid's algorithm

Highest Common Factor of 89,657,160,220 is 1

Step 1: Since 657 > 89, we apply the division lemma to 657 and 89, to get

657 = 89 x 7 + 34

Step 2: Since the reminder 89 ≠ 0, we apply division lemma to 34 and 89, to get

89 = 34 x 2 + 21

Step 3: We consider the new divisor 34 and the new remainder 21, and apply the division lemma to get

34 = 21 x 1 + 13

We consider the new divisor 21 and the new remainder 13,and apply the division lemma to get

21 = 13 x 1 + 8

We consider the new divisor 13 and the new remainder 8,and apply the division lemma to get

13 = 8 x 1 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 89 and 657 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(21,13) = HCF(34,21) = HCF(89,34) = HCF(657,89) .

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

Step 1: Since 160 > 1, we apply the division lemma to 160 and 1, to get

160 = 1 x 160 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 160 is 1

Notice that 1 = HCF(160,1) .

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

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

220 = 1 x 220 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 220 is 1

Notice that 1 = HCF(220,1) .

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Frequently Asked Questions on HCF of 89, 657, 160, 220 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 89, 657, 160, 220?

Answer: HCF of 89, 657, 160, 220 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 89, 657, 160, 220 using Euclid's Algorithm?

Answer: For arbitrary numbers 89, 657, 160, 220 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.