Highest Common Factor of 259, 150, 222 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, 150, 222 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 259, 150, 222 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, 150, 222 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, 150, 222 is 1.

HCF(259, 150, 222) = 1

HCF of 259, 150, 222 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, 150, 222 is 1.

Highest Common Factor of 259,150,222 using Euclid's algorithm

Highest Common Factor of 259,150,222 is 1

Step 1: Since 259 > 150, we apply the division lemma to 259 and 150, to get

259 = 150 x 1 + 109

Step 2: Since the reminder 150 ≠ 0, we apply division lemma to 109 and 150, to get

150 = 109 x 1 + 41

Step 3: We consider the new divisor 109 and the new remainder 41, and apply the division lemma to get

109 = 41 x 2 + 27

We consider the new divisor 41 and the new remainder 27,and apply the division lemma to get

41 = 27 x 1 + 14

We consider the new divisor 27 and the new remainder 14,and apply the division lemma to get

27 = 14 x 1 + 13

We consider the new divisor 14 and the new remainder 13,and apply the division lemma to get

14 = 13 x 1 + 1

We consider the new divisor 13 and the new remainder 1,and apply the division lemma to get

13 = 1 x 13 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 259 and 150 is 1

Notice that 1 = HCF(13,1) = HCF(14,13) = HCF(27,14) = HCF(41,27) = HCF(109,41) = HCF(150,109) = HCF(259,150) .

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

Step 1: Since 222 > 1, we apply the division lemma to 222 and 1, to get

222 = 1 x 222 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 222 is 1

Notice that 1 = HCF(222,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 259, 150, 222 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, 150, 222?

Answer: HCF of 259, 150, 222 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 259, 150, 222 using Euclid's Algorithm?

Answer: For arbitrary numbers 259, 150, 222 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.