Highest Common Factor of 203, 928, 460 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 203, 928, 460 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 203, 928, 460 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 203, 928, 460 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 203, 928, 460 is 1.

HCF(203, 928, 460) = 1

HCF of 203, 928, 460 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 203, 928, 460 is 1.

Highest Common Factor of 203,928,460 using Euclid's algorithm

Highest Common Factor of 203,928,460 is 1

Step 1: Since 928 > 203, we apply the division lemma to 928 and 203, to get

928 = 203 x 4 + 116

Step 2: Since the reminder 203 ≠ 0, we apply division lemma to 116 and 203, to get

203 = 116 x 1 + 87

Step 3: We consider the new divisor 116 and the new remainder 87, and apply the division lemma to get

116 = 87 x 1 + 29

We consider the new divisor 87 and the new remainder 29, and apply the division lemma to get

87 = 29 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 29, the HCF of 203 and 928 is 29

Notice that 29 = HCF(87,29) = HCF(116,87) = HCF(203,116) = HCF(928,203) .

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

Step 1: Since 460 > 29, we apply the division lemma to 460 and 29, to get

460 = 29 x 15 + 25

Step 2: Since the reminder 29 ≠ 0, we apply division lemma to 25 and 29, to get

29 = 25 x 1 + 4

Step 3: We consider the new divisor 25 and the new remainder 4, and apply the division lemma to get

25 = 4 x 6 + 1

We consider the new divisor 4 and the new remainder 1, and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 29 and 460 is 1

Notice that 1 = HCF(4,1) = HCF(25,4) = HCF(29,25) = HCF(460,29) .

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Frequently Asked Questions on HCF of 203, 928, 460 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 203, 928, 460?

Answer: HCF of 203, 928, 460 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 203, 928, 460 using Euclid's Algorithm?

Answer: For arbitrary numbers 203, 928, 460 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.