Highest Common Factor of 918, 588, 413 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 918, 588, 413 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 918, 588, 413 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 918, 588, 413 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 918, 588, 413 is 1.

HCF(918, 588, 413) = 1

HCF of 918, 588, 413 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 918, 588, 413 is 1.

Highest Common Factor of 918,588,413 using Euclid's algorithm

Highest Common Factor of 918,588,413 is 1

Step 1: Since 918 > 588, we apply the division lemma to 918 and 588, to get

918 = 588 x 1 + 330

Step 2: Since the reminder 588 ≠ 0, we apply division lemma to 330 and 588, to get

588 = 330 x 1 + 258

Step 3: We consider the new divisor 330 and the new remainder 258, and apply the division lemma to get

330 = 258 x 1 + 72

We consider the new divisor 258 and the new remainder 72,and apply the division lemma to get

258 = 72 x 3 + 42

We consider the new divisor 72 and the new remainder 42,and apply the division lemma to get

72 = 42 x 1 + 30

We consider the new divisor 42 and the new remainder 30,and apply the division lemma to get

42 = 30 x 1 + 12

We consider the new divisor 30 and the new remainder 12,and apply the division lemma to get

30 = 12 x 2 + 6

We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get

12 = 6 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 918 and 588 is 6

Notice that 6 = HCF(12,6) = HCF(30,12) = HCF(42,30) = HCF(72,42) = HCF(258,72) = HCF(330,258) = HCF(588,330) = HCF(918,588) .

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

Step 1: Since 413 > 6, we apply the division lemma to 413 and 6, to get

413 = 6 x 68 + 5

Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 5 and 6, to get

6 = 5 x 1 + 1

Step 3: We consider the new divisor 5 and the new remainder 1, and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6 and 413 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(413,6) .

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Frequently Asked Questions on HCF of 918, 588, 413 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 918, 588, 413?

Answer: HCF of 918, 588, 413 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 918, 588, 413 using Euclid's Algorithm?

Answer: For arbitrary numbers 918, 588, 413 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.