Highest Common Factor of 720, 992, 917 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 720, 992, 917 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 720, 992, 917 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 720, 992, 917 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 720, 992, 917 is 1.

HCF(720, 992, 917) = 1

HCF of 720, 992, 917 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 720, 992, 917 is 1.

Highest Common Factor of 720,992,917 using Euclid's algorithm

Highest Common Factor of 720,992,917 is 1

Step 1: Since 992 > 720, we apply the division lemma to 992 and 720, to get

992 = 720 x 1 + 272

Step 2: Since the reminder 720 ≠ 0, we apply division lemma to 272 and 720, to get

720 = 272 x 2 + 176

Step 3: We consider the new divisor 272 and the new remainder 176, and apply the division lemma to get

272 = 176 x 1 + 96

We consider the new divisor 176 and the new remainder 96,and apply the division lemma to get

176 = 96 x 1 + 80

We consider the new divisor 96 and the new remainder 80,and apply the division lemma to get

96 = 80 x 1 + 16

We consider the new divisor 80 and the new remainder 16,and apply the division lemma to get

80 = 16 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 720 and 992 is 16

Notice that 16 = HCF(80,16) = HCF(96,80) = HCF(176,96) = HCF(272,176) = HCF(720,272) = HCF(992,720) .

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

Step 1: Since 917 > 16, we apply the division lemma to 917 and 16, to get

917 = 16 x 57 + 5

Step 2: Since the reminder 16 ≠ 0, we apply division lemma to 5 and 16, to get

16 = 5 x 3 + 1

Step 3: We consider the new divisor 5 and the new remainder 1, and apply the division lemma 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 16 and 917 is 1

Notice that 1 = HCF(5,1) = HCF(16,5) = HCF(917,16) .

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Frequently Asked Questions on HCF of 720, 992, 917 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 720, 992, 917?

Answer: HCF of 720, 992, 917 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 720, 992, 917 using Euclid's Algorithm?

Answer: For arbitrary numbers 720, 992, 917 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.