Highest Common Factor of 259, 360, 122 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 259, 360, 122 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 259, 360, 122 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 259, 360, 122 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 259, 360, 122 is 1.

HCF(259, 360, 122) = 1

HCF of 259, 360, 122 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 259, 360, 122 is 1.

Highest Common Factor of 259,360,122 using Euclid's algorithm

Highest Common Factor of 259,360,122 is 1

Step 1: Since 360 > 259, we apply the division lemma to 360 and 259, to get

360 = 259 x 1 + 101

Step 2: Since the reminder 259 ≠ 0, we apply division lemma to 101 and 259, to get

259 = 101 x 2 + 57

Step 3: We consider the new divisor 101 and the new remainder 57, and apply the division lemma to get

101 = 57 x 1 + 44

We consider the new divisor 57 and the new remainder 44,and apply the division lemma to get

57 = 44 x 1 + 13

We consider the new divisor 44 and the new remainder 13,and apply the division lemma to get

44 = 13 x 3 + 5

We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get

13 = 5 x 2 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

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 259 and 360 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(44,13) = HCF(57,44) = HCF(101,57) = HCF(259,101) = HCF(360,259) .

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

Step 1: Since 122 > 1, we apply the division lemma to 122 and 1, to get

122 = 1 x 122 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 122 is 1

Notice that 1 = HCF(122,1) .

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Frequently Asked Questions on HCF of 259, 360, 122 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 259, 360, 122?

Answer: HCF of 259, 360, 122 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 259, 360, 122 using Euclid's Algorithm?

Answer: For arbitrary numbers 259, 360, 122 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.