Highest Common Factor of 558, 988, 299 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 558, 988, 299 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 558, 988, 299 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 558, 988, 299 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 558, 988, 299 is 1.

HCF(558, 988, 299) = 1

HCF of 558, 988, 299 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 558, 988, 299 is 1.

Highest Common Factor of 558,988,299 using Euclid's algorithm

Highest Common Factor of 558,988,299 is 1

Step 1: Since 988 > 558, we apply the division lemma to 988 and 558, to get

988 = 558 x 1 + 430

Step 2: Since the reminder 558 ≠ 0, we apply division lemma to 430 and 558, to get

558 = 430 x 1 + 128

Step 3: We consider the new divisor 430 and the new remainder 128, and apply the division lemma to get

430 = 128 x 3 + 46

We consider the new divisor 128 and the new remainder 46,and apply the division lemma to get

128 = 46 x 2 + 36

We consider the new divisor 46 and the new remainder 36,and apply the division lemma to get

46 = 36 x 1 + 10

We consider the new divisor 36 and the new remainder 10,and apply the division lemma to get

36 = 10 x 3 + 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 558 and 988 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(36,10) = HCF(46,36) = HCF(128,46) = HCF(430,128) = HCF(558,430) = HCF(988,558) .

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

Step 1: Since 299 > 2, we apply the division lemma to 299 and 2, to get

299 = 2 x 149 + 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 299 is 1

Notice that 1 = HCF(2,1) = HCF(299,2) .

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Frequently Asked Questions on HCF of 558, 988, 299 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 558, 988, 299?

Answer: HCF of 558, 988, 299 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 558, 988, 299 using Euclid's Algorithm?

Answer: For arbitrary numbers 558, 988, 299 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.