Highest Common Factor of 176, 2032, 4589 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 176, 2032, 4589 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 176, 2032, 4589 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 176, 2032, 4589 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 176, 2032, 4589 is 1.

HCF(176, 2032, 4589) = 1

HCF of 176, 2032, 4589 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 176, 2032, 4589 is 1.

Highest Common Factor of 176,2032,4589 using Euclid's algorithm

Highest Common Factor of 176,2032,4589 is 1

Step 1: Since 2032 > 176, we apply the division lemma to 2032 and 176, to get

2032 = 176 x 11 + 96

Step 2: Since the reminder 176 ≠ 0, we apply division lemma to 96 and 176, to get

176 = 96 x 1 + 80

Step 3: We consider the new divisor 96 and the new remainder 80, and apply the division lemma to get

96 = 80 x 1 + 16

We consider the new divisor 80 and the new remainder 16, and apply the division lemma to get

80 = 16 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 176 and 2032 is 16

Notice that 16 = HCF(80,16) = HCF(96,80) = HCF(176,96) = HCF(2032,176) .

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

Step 1: Since 4589 > 16, we apply the division lemma to 4589 and 16, to get

4589 = 16 x 286 + 13

Step 2: Since the reminder 16 ≠ 0, we apply division lemma to 13 and 16, to get

16 = 13 x 1 + 3

Step 3: We consider the new divisor 13 and the new remainder 3, and apply the division lemma to get

13 = 3 x 4 + 1

We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 16 and 4589 is 1

Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(16,13) = HCF(4589,16) .

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Frequently Asked Questions on HCF of 176, 2032, 4589 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 176, 2032, 4589?

Answer: HCF of 176, 2032, 4589 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 176, 2032, 4589 using Euclid's Algorithm?

Answer: For arbitrary numbers 176, 2032, 4589 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.