Highest Common Factor of 998, 577, 261 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, 577, 261 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 998, 577, 261 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, 577, 261 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, 577, 261 is 1.

HCF(998, 577, 261) = 1

HCF of 998, 577, 261 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, 577, 261 is 1.

Highest Common Factor of 998,577,261 using Euclid's algorithm

Highest Common Factor of 998,577,261 is 1

Step 1: Since 998 > 577, we apply the division lemma to 998 and 577, to get

998 = 577 x 1 + 421

Step 2: Since the reminder 577 ≠ 0, we apply division lemma to 421 and 577, to get

577 = 421 x 1 + 156

Step 3: We consider the new divisor 421 and the new remainder 156, and apply the division lemma to get

421 = 156 x 2 + 109

We consider the new divisor 156 and the new remainder 109,and apply the division lemma to get

156 = 109 x 1 + 47

We consider the new divisor 109 and the new remainder 47,and apply the division lemma to get

109 = 47 x 2 + 15

We consider the new divisor 47 and the new remainder 15,and apply the division lemma to get

47 = 15 x 3 + 2

We consider the new divisor 15 and the new remainder 2,and apply the division lemma to get

15 = 2 x 7 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 998 and 577 is 1

Notice that 1 = HCF(2,1) = HCF(15,2) = HCF(47,15) = HCF(109,47) = HCF(156,109) = HCF(421,156) = HCF(577,421) = HCF(998,577) .

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

Step 1: Since 261 > 1, we apply the division lemma to 261 and 1, to get

261 = 1 x 261 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 261 is 1

Notice that 1 = HCF(261,1) .

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Frequently Asked Questions on HCF of 998, 577, 261 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, 577, 261?

Answer: HCF of 998, 577, 261 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 998, 577, 261 using Euclid's Algorithm?

Answer: For arbitrary numbers 998, 577, 261 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.