Highest Common Factor of 336, 998, 251 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 336, 998, 251 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 336, 998, 251 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 336, 998, 251 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 336, 998, 251 is 1.

HCF(336, 998, 251) = 1

HCF of 336, 998, 251 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 336, 998, 251 is 1.

Highest Common Factor of 336,998,251 using Euclid's algorithm

Highest Common Factor of 336,998,251 is 1

Step 1: Since 998 > 336, we apply the division lemma to 998 and 336, to get

998 = 336 x 2 + 326

Step 2: Since the reminder 336 ≠ 0, we apply division lemma to 326 and 336, to get

336 = 326 x 1 + 10

Step 3: We consider the new divisor 326 and the new remainder 10, and apply the division lemma to get

326 = 10 x 32 + 6

We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get

10 = 6 x 1 + 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 336 and 998 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(326,10) = HCF(336,326) = HCF(998,336) .

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

Step 1: Since 251 > 2, we apply the division lemma to 251 and 2, to get

251 = 2 x 125 + 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 251 is 1

Notice that 1 = HCF(2,1) = HCF(251,2) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 336, 998, 251 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 336, 998, 251?

Answer: HCF of 336, 998, 251 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 336, 998, 251 using Euclid's Algorithm?

Answer: For arbitrary numbers 336, 998, 251 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.