Highest Common Factor of 998, 278, 899 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, 278, 899 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 998, 278, 899 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, 278, 899 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, 278, 899 is 1.

HCF(998, 278, 899) = 1

HCF of 998, 278, 899 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, 278, 899 is 1.

Highest Common Factor of 998,278,899 using Euclid's algorithm

Highest Common Factor of 998,278,899 is 1

Step 1: Since 998 > 278, we apply the division lemma to 998 and 278, to get

998 = 278 x 3 + 164

Step 2: Since the reminder 278 ≠ 0, we apply division lemma to 164 and 278, to get

278 = 164 x 1 + 114

Step 3: We consider the new divisor 164 and the new remainder 114, and apply the division lemma to get

164 = 114 x 1 + 50

We consider the new divisor 114 and the new remainder 50,and apply the division lemma to get

114 = 50 x 2 + 14

We consider the new divisor 50 and the new remainder 14,and apply the division lemma to get

50 = 14 x 3 + 8

We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get

14 = 8 x 1 + 6

We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get

8 = 6 x 1 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 998 and 278 is 2

Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(50,14) = HCF(114,50) = HCF(164,114) = HCF(278,164) = HCF(998,278) .

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

Step 1: Since 899 > 2, we apply the division lemma to 899 and 2, to get

899 = 2 x 449 + 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 899 is 1

Notice that 1 = HCF(2,1) = HCF(899,2) .

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Frequently Asked Questions on HCF of 998, 278, 899 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, 278, 899?

Answer: HCF of 998, 278, 899 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 998, 278, 899 using Euclid's Algorithm?

Answer: For arbitrary numbers 998, 278, 899 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.