Highest Common Factor of 916, 568, 173 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 916, 568, 173 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 916, 568, 173 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 916, 568, 173 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 916, 568, 173 is 1.

HCF(916, 568, 173) = 1

HCF of 916, 568, 173 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 916, 568, 173 is 1.

Highest Common Factor of 916,568,173 using Euclid's algorithm

Highest Common Factor of 916,568,173 is 1

Step 1: Since 916 > 568, we apply the division lemma to 916 and 568, to get

916 = 568 x 1 + 348

Step 2: Since the reminder 568 ≠ 0, we apply division lemma to 348 and 568, to get

568 = 348 x 1 + 220

Step 3: We consider the new divisor 348 and the new remainder 220, and apply the division lemma to get

348 = 220 x 1 + 128

We consider the new divisor 220 and the new remainder 128,and apply the division lemma to get

220 = 128 x 1 + 92

We consider the new divisor 128 and the new remainder 92,and apply the division lemma to get

128 = 92 x 1 + 36

We consider the new divisor 92 and the new remainder 36,and apply the division lemma to get

92 = 36 x 2 + 20

We consider the new divisor 36 and the new remainder 20,and apply the division lemma to get

36 = 20 x 1 + 16

We consider the new divisor 20 and the new remainder 16,and apply the division lemma to get

20 = 16 x 1 + 4

We consider the new divisor 16 and the new remainder 4,and apply the division lemma to get

16 = 4 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 916 and 568 is 4

Notice that 4 = HCF(16,4) = HCF(20,16) = HCF(36,20) = HCF(92,36) = HCF(128,92) = HCF(220,128) = HCF(348,220) = HCF(568,348) = HCF(916,568) .

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

Step 1: Since 173 > 4, we apply the division lemma to 173 and 4, to get

173 = 4 x 43 + 1

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, 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 4 and 173 is 1

Notice that 1 = HCF(4,1) = HCF(173,4) .

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Frequently Asked Questions on HCF of 916, 568, 173 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 916, 568, 173?

Answer: HCF of 916, 568, 173 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 916, 568, 173 using Euclid's Algorithm?

Answer: For arbitrary numbers 916, 568, 173 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.