Highest Common Factor of 171, 305, 150 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 171, 305, 150 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 171, 305, 150 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 171, 305, 150 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 171, 305, 150 is 1.

HCF(171, 305, 150) = 1

HCF of 171, 305, 150 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 171, 305, 150 is 1.

Highest Common Factor of 171,305,150 using Euclid's algorithm

Highest Common Factor of 171,305,150 is 1

Step 1: Since 305 > 171, we apply the division lemma to 305 and 171, to get

305 = 171 x 1 + 134

Step 2: Since the reminder 171 ≠ 0, we apply division lemma to 134 and 171, to get

171 = 134 x 1 + 37

Step 3: We consider the new divisor 134 and the new remainder 37, and apply the division lemma to get

134 = 37 x 3 + 23

We consider the new divisor 37 and the new remainder 23,and apply the division lemma to get

37 = 23 x 1 + 14

We consider the new divisor 23 and the new remainder 14,and apply the division lemma to get

23 = 14 x 1 + 9

We consider the new divisor 14 and the new remainder 9,and apply the division lemma to get

14 = 9 x 1 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 171 and 305 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(14,9) = HCF(23,14) = HCF(37,23) = HCF(134,37) = HCF(171,134) = HCF(305,171) .

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

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

150 = 1 x 150 + 0

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

Notice that 1 = HCF(150,1) .

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Frequently Asked Questions on HCF of 171, 305, 150 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 171, 305, 150?

Answer: HCF of 171, 305, 150 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 171, 305, 150 using Euclid's Algorithm?

Answer: For arbitrary numbers 171, 305, 150 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.