Highest Common Factor of 998, 342, 391 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 998, 342, 391 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 998, 342, 391 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 998, 342, 391 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 998, 342, 391 is 1.

HCF(998, 342, 391) = 1

HCF of 998, 342, 391 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 998, 342, 391 is 1.

Highest Common Factor of 998,342,391 using Euclid's algorithm

Highest Common Factor of 998,342,391 is 1

Step 1: Since 998 > 342, we apply the division lemma to 998 and 342, to get

998 = 342 x 2 + 314

Step 2: Since the reminder 342 ≠ 0, we apply division lemma to 314 and 342, to get

342 = 314 x 1 + 28

Step 3: We consider the new divisor 314 and the new remainder 28, and apply the division lemma to get

314 = 28 x 11 + 6

We consider the new divisor 28 and the new remainder 6,and apply the division lemma to get

28 = 6 x 4 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 998 and 342 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(28,6) = HCF(314,28) = HCF(342,314) = HCF(998,342) .

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

Step 1: Since 391 > 2, we apply the division lemma to 391 and 2, to get

391 = 2 x 195 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 391 is 1

Notice that 1 = HCF(2,1) = HCF(391,2) .

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Frequently Asked Questions on HCF of 998, 342, 391 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 998, 342, 391?

Answer: HCF of 998, 342, 391 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 998, 342, 391 using Euclid's Algorithm?

Answer: For arbitrary numbers 998, 342, 391 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.