Highest Common Factor of 17, 258 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 17, 258 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 17, 258 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 17, 258 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 17, 258 is 1.

HCF(17, 258) = 1

HCF of 17, 258 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 17, 258 is 1.

Highest Common Factor of 17,258 using Euclid's algorithm

Highest Common Factor of 17,258 is 1

Step 1: Since 258 > 17, we apply the division lemma to 258 and 17, to get

258 = 17 x 15 + 3

Step 2: Since the reminder 17 ≠ 0, we apply division lemma to 3 and 17, to get

17 = 3 x 5 + 2

Step 3: We consider the new divisor 3 and the new remainder 2, and apply the division lemma to get

3 = 2 x 1 + 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 17 and 258 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(17,3) = HCF(258,17) .

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Frequently Asked Questions on HCF of 17, 258 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 17, 258?

Answer: HCF of 17, 258 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 17, 258 using Euclid's Algorithm?

Answer: For arbitrary numbers 17, 258 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.