Highest Common Factor of 726, 975, 916 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 726, 975, 916 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 726, 975, 916 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 726, 975, 916 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 726, 975, 916 is 1.

HCF(726, 975, 916) = 1

HCF of 726, 975, 916 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 726, 975, 916 is 1.

Highest Common Factor of 726,975,916 using Euclid's algorithm

Highest Common Factor of 726,975,916 is 1

Step 1: Since 975 > 726, we apply the division lemma to 975 and 726, to get

975 = 726 x 1 + 249

Step 2: Since the reminder 726 ≠ 0, we apply division lemma to 249 and 726, to get

726 = 249 x 2 + 228

Step 3: We consider the new divisor 249 and the new remainder 228, and apply the division lemma to get

249 = 228 x 1 + 21

We consider the new divisor 228 and the new remainder 21,and apply the division lemma to get

228 = 21 x 10 + 18

We consider the new divisor 21 and the new remainder 18,and apply the division lemma to get

21 = 18 x 1 + 3

We consider the new divisor 18 and the new remainder 3,and apply the division lemma to get

18 = 3 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 726 and 975 is 3

Notice that 3 = HCF(18,3) = HCF(21,18) = HCF(228,21) = HCF(249,228) = HCF(726,249) = HCF(975,726) .

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

Step 1: Since 916 > 3, we apply the division lemma to 916 and 3, to get

916 = 3 x 305 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 916 is 1

Notice that 1 = HCF(3,1) = HCF(916,3) .

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Frequently Asked Questions on HCF of 726, 975, 916 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 726, 975, 916?

Answer: HCF of 726, 975, 916 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 726, 975, 916 using Euclid's Algorithm?

Answer: For arbitrary numbers 726, 975, 916 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.