Highest Common Factor of 415, 130, 203, 914 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 415, 130, 203, 914 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 415, 130, 203, 914 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 415, 130, 203, 914 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 415, 130, 203, 914 is 1.

HCF(415, 130, 203, 914) = 1

HCF of 415, 130, 203, 914 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 415, 130, 203, 914 is 1.

Highest Common Factor of 415,130,203,914 using Euclid's algorithm

Highest Common Factor of 415,130,203,914 is 1

Step 1: Since 415 > 130, we apply the division lemma to 415 and 130, to get

415 = 130 x 3 + 25

Step 2: Since the reminder 130 ≠ 0, we apply division lemma to 25 and 130, to get

130 = 25 x 5 + 5

Step 3: We consider the new divisor 25 and the new remainder 5, and apply the division lemma to get

25 = 5 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 415 and 130 is 5

Notice that 5 = HCF(25,5) = HCF(130,25) = HCF(415,130) .

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

Step 1: Since 203 > 5, we apply the division lemma to 203 and 5, to get

203 = 5 x 40 + 3

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get

5 = 3 x 1 + 2

Step 3: 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 5 and 203 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(203,5) .

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

Step 1: Since 914 > 1, we apply the division lemma to 914 and 1, to get

914 = 1 x 914 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 914 is 1

Notice that 1 = HCF(914,1) .

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Frequently Asked Questions on HCF of 415, 130, 203, 914 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 415, 130, 203, 914?

Answer: HCF of 415, 130, 203, 914 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 415, 130, 203, 914 using Euclid's Algorithm?

Answer: For arbitrary numbers 415, 130, 203, 914 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.