Highest Common Factor of 760, 315, 296 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 760, 315, 296 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 760, 315, 296 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 760, 315, 296 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 760, 315, 296 is 1.

HCF(760, 315, 296) = 1

HCF of 760, 315, 296 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 760, 315, 296 is 1.

Highest Common Factor of 760,315,296 using Euclid's algorithm

Highest Common Factor of 760,315,296 is 1

Step 1: Since 760 > 315, we apply the division lemma to 760 and 315, to get

760 = 315 x 2 + 130

Step 2: Since the reminder 315 ≠ 0, we apply division lemma to 130 and 315, to get

315 = 130 x 2 + 55

Step 3: We consider the new divisor 130 and the new remainder 55, and apply the division lemma to get

130 = 55 x 2 + 20

We consider the new divisor 55 and the new remainder 20,and apply the division lemma to get

55 = 20 x 2 + 15

We consider the new divisor 20 and the new remainder 15,and apply the division lemma to get

20 = 15 x 1 + 5

We consider the new divisor 15 and the new remainder 5,and apply the division lemma to get

15 = 5 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 760 and 315 is 5

Notice that 5 = HCF(15,5) = HCF(20,15) = HCF(55,20) = HCF(130,55) = HCF(315,130) = HCF(760,315) .

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

Step 1: Since 296 > 5, we apply the division lemma to 296 and 5, to get

296 = 5 x 59 + 1

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 1 and 5, to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 296 is 1

Notice that 1 = HCF(5,1) = HCF(296,5) .

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Frequently Asked Questions on HCF of 760, 315, 296 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 760, 315, 296?

Answer: HCF of 760, 315, 296 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 760, 315, 296 using Euclid's Algorithm?

Answer: For arbitrary numbers 760, 315, 296 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.