Highest Common Factor of 704, 264, 515 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 704, 264, 515 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 704, 264, 515 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 704, 264, 515 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 704, 264, 515 is 1.

HCF(704, 264, 515) = 1

HCF of 704, 264, 515 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 704, 264, 515 is 1.

Highest Common Factor of 704,264,515 using Euclid's algorithm

Highest Common Factor of 704,264,515 is 1

Step 1: Since 704 > 264, we apply the division lemma to 704 and 264, to get

704 = 264 x 2 + 176

Step 2: Since the reminder 264 ≠ 0, we apply division lemma to 176 and 264, to get

264 = 176 x 1 + 88

Step 3: We consider the new divisor 176 and the new remainder 88, and apply the division lemma to get

176 = 88 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 88, the HCF of 704 and 264 is 88

Notice that 88 = HCF(176,88) = HCF(264,176) = HCF(704,264) .

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

Step 1: Since 515 > 88, we apply the division lemma to 515 and 88, to get

515 = 88 x 5 + 75

Step 2: Since the reminder 88 ≠ 0, we apply division lemma to 75 and 88, to get

88 = 75 x 1 + 13

Step 3: We consider the new divisor 75 and the new remainder 13, and apply the division lemma to get

75 = 13 x 5 + 10

We consider the new divisor 13 and the new remainder 10,and apply the division lemma to get

13 = 10 x 1 + 3

We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get

10 = 3 x 3 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 88 and 515 is 1

Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(13,10) = HCF(75,13) = HCF(88,75) = HCF(515,88) .

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Frequently Asked Questions on HCF of 704, 264, 515 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 704, 264, 515?

Answer: HCF of 704, 264, 515 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 704, 264, 515 using Euclid's Algorithm?

Answer: For arbitrary numbers 704, 264, 515 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.