Highest Common Factor of 412, 304, 515 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 412, 304, 515 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 412, 304, 515 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 412, 304, 515 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 412, 304, 515 is 1.

HCF(412, 304, 515) = 1

HCF of 412, 304, 515 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 412, 304, 515 is 1.

Highest Common Factor of 412,304,515 using Euclid's algorithm

Highest Common Factor of 412,304,515 is 1

Step 1: Since 412 > 304, we apply the division lemma to 412 and 304, to get

412 = 304 x 1 + 108

Step 2: Since the reminder 304 ≠ 0, we apply division lemma to 108 and 304, to get

304 = 108 x 2 + 88

Step 3: We consider the new divisor 108 and the new remainder 88, and apply the division lemma to get

108 = 88 x 1 + 20

We consider the new divisor 88 and the new remainder 20,and apply the division lemma to get

88 = 20 x 4 + 8

We consider the new divisor 20 and the new remainder 8,and apply the division lemma to get

20 = 8 x 2 + 4

We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get

8 = 4 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 412 and 304 is 4

Notice that 4 = HCF(8,4) = HCF(20,8) = HCF(88,20) = HCF(108,88) = HCF(304,108) = HCF(412,304) .

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

Step 1: Since 515 > 4, we apply the division lemma to 515 and 4, to get

515 = 4 x 128 + 3

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get

4 = 3 x 1 + 1

Step 3: 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 4 and 515 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(515,4) .

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Frequently Asked Questions on HCF of 412, 304, 515 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 412, 304, 515?

Answer: HCF of 412, 304, 515 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 412, 304, 515 using Euclid's Algorithm?

Answer: For arbitrary numbers 412, 304, 515 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.