Highest Common Factor of 258, 477, 698 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 258, 477, 698 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 258, 477, 698 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 258, 477, 698 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 258, 477, 698 is 1.

HCF(258, 477, 698) = 1

HCF of 258, 477, 698 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 258, 477, 698 is 1.

Highest Common Factor of 258,477,698 using Euclid's algorithm

Highest Common Factor of 258,477,698 is 1

Step 1: Since 477 > 258, we apply the division lemma to 477 and 258, to get

477 = 258 x 1 + 219

Step 2: Since the reminder 258 ≠ 0, we apply division lemma to 219 and 258, to get

258 = 219 x 1 + 39

Step 3: We consider the new divisor 219 and the new remainder 39, and apply the division lemma to get

219 = 39 x 5 + 24

We consider the new divisor 39 and the new remainder 24,and apply the division lemma to get

39 = 24 x 1 + 15

We consider the new divisor 24 and the new remainder 15,and apply the division lemma to get

24 = 15 x 1 + 9

We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get

15 = 9 x 1 + 6

We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get

9 = 6 x 1 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 258 and 477 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(24,15) = HCF(39,24) = HCF(219,39) = HCF(258,219) = HCF(477,258) .

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

Step 1: Since 698 > 3, we apply the division lemma to 698 and 3, to get

698 = 3 x 232 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: 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 3 and 698 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(698,3) .

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Frequently Asked Questions on HCF of 258, 477, 698 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 258, 477, 698?

Answer: HCF of 258, 477, 698 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 258, 477, 698 using Euclid's Algorithm?

Answer: For arbitrary numbers 258, 477, 698 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.