Highest Common Factor of 165, 296, 430 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 165, 296, 430 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 165, 296, 430 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 165, 296, 430 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 165, 296, 430 is 1.

HCF(165, 296, 430) = 1

HCF of 165, 296, 430 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 165, 296, 430 is 1.

Highest Common Factor of 165,296,430 using Euclid's algorithm

Highest Common Factor of 165,296,430 is 1

Step 1: Since 296 > 165, we apply the division lemma to 296 and 165, to get

296 = 165 x 1 + 131

Step 2: Since the reminder 165 ≠ 0, we apply division lemma to 131 and 165, to get

165 = 131 x 1 + 34

Step 3: We consider the new divisor 131 and the new remainder 34, and apply the division lemma to get

131 = 34 x 3 + 29

We consider the new divisor 34 and the new remainder 29,and apply the division lemma to get

34 = 29 x 1 + 5

We consider the new divisor 29 and the new remainder 5,and apply the division lemma to get

29 = 5 x 5 + 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 165 and 296 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(29,5) = HCF(34,29) = HCF(131,34) = HCF(165,131) = HCF(296,165) .

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

Step 1: Since 430 > 1, we apply the division lemma to 430 and 1, to get

430 = 1 x 430 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 430 is 1

Notice that 1 = HCF(430,1) .

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Frequently Asked Questions on HCF of 165, 296, 430 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 165, 296, 430?

Answer: HCF of 165, 296, 430 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 165, 296, 430 using Euclid's Algorithm?

Answer: For arbitrary numbers 165, 296, 430 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.