Highest Common Factor of 274, 176, 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 274, 176, 916 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 274, 176, 916 is 2 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 274, 176, 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 274, 176, 916 is 2.

HCF(274, 176, 916) = 2

HCF of 274, 176, 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 274, 176, 916 is 2.

Highest Common Factor of 274,176,916 using Euclid's algorithm

Highest Common Factor of 274,176,916 is 2

Step 1: Since 274 > 176, we apply the division lemma to 274 and 176, to get

274 = 176 x 1 + 98

Step 2: Since the reminder 176 ≠ 0, we apply division lemma to 98 and 176, to get

176 = 98 x 1 + 78

Step 3: We consider the new divisor 98 and the new remainder 78, and apply the division lemma to get

98 = 78 x 1 + 20

We consider the new divisor 78 and the new remainder 20,and apply the division lemma to get

78 = 20 x 3 + 18

We consider the new divisor 20 and the new remainder 18,and apply the division lemma to get

20 = 18 x 1 + 2

We consider the new divisor 18 and the new remainder 2,and apply the division lemma to get

18 = 2 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 274 and 176 is 2

Notice that 2 = HCF(18,2) = HCF(20,18) = HCF(78,20) = HCF(98,78) = HCF(176,98) = HCF(274,176) .

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

Step 1: Since 916 > 2, we apply the division lemma to 916 and 2, to get

916 = 2 x 458 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 916 is 2

Notice that 2 = HCF(916,2) .

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Frequently Asked Questions on HCF of 274, 176, 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 274, 176, 916?

Answer: HCF of 274, 176, 916 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 274, 176, 916 using Euclid's Algorithm?

Answer: For arbitrary numbers 274, 176, 916 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.