Highest Common Factor of 264, 430, 17 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 264, 430, 17 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 264, 430, 17 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 264, 430, 17 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 264, 430, 17 is 1.

HCF(264, 430, 17) = 1

HCF of 264, 430, 17 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 264, 430, 17 is 1.

Highest Common Factor of 264,430,17 using Euclid's algorithm

Highest Common Factor of 264,430,17 is 1

Step 1: Since 430 > 264, we apply the division lemma to 430 and 264, to get

430 = 264 x 1 + 166

Step 2: Since the reminder 264 ≠ 0, we apply division lemma to 166 and 264, to get

264 = 166 x 1 + 98

Step 3: We consider the new divisor 166 and the new remainder 98, and apply the division lemma to get

166 = 98 x 1 + 68

We consider the new divisor 98 and the new remainder 68,and apply the division lemma to get

98 = 68 x 1 + 30

We consider the new divisor 68 and the new remainder 30,and apply the division lemma to get

68 = 30 x 2 + 8

We consider the new divisor 30 and the new remainder 8,and apply the division lemma to get

30 = 8 x 3 + 6

We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get

8 = 6 x 1 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 264 and 430 is 2

Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(30,8) = HCF(68,30) = HCF(98,68) = HCF(166,98) = HCF(264,166) = HCF(430,264) .

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

Step 1: Since 17 > 2, we apply the division lemma to 17 and 2, to get

17 = 2 x 8 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 17 is 1

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

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Frequently Asked Questions on HCF of 264, 430, 17 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 264, 430, 17?

Answer: HCF of 264, 430, 17 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 264, 430, 17 using Euclid's Algorithm?

Answer: For arbitrary numbers 264, 430, 17 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.