Highest Common Factor of 312, 266, 110 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 312, 266, 110 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 312, 266, 110 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 312, 266, 110 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 312, 266, 110 is 2.

HCF(312, 266, 110) = 2

HCF of 312, 266, 110 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 312, 266, 110 is 2.

Highest Common Factor of 312,266,110 using Euclid's algorithm

Highest Common Factor of 312,266,110 is 2

Step 1: Since 312 > 266, we apply the division lemma to 312 and 266, to get

312 = 266 x 1 + 46

Step 2: Since the reminder 266 ≠ 0, we apply division lemma to 46 and 266, to get

266 = 46 x 5 + 36

Step 3: We consider the new divisor 46 and the new remainder 36, and apply the division lemma to get

46 = 36 x 1 + 10

We consider the new divisor 36 and the new remainder 10,and apply the division lemma to get

36 = 10 x 3 + 6

We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get

10 = 6 x 1 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 312 and 266 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(36,10) = HCF(46,36) = HCF(266,46) = HCF(312,266) .

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

Step 1: Since 110 > 2, we apply the division lemma to 110 and 2, to get

110 = 2 x 55 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 110 is 2

Notice that 2 = HCF(110,2) .

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Frequently Asked Questions on HCF of 312, 266, 110 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 312, 266, 110?

Answer: HCF of 312, 266, 110 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 312, 266, 110 using Euclid's Algorithm?

Answer: For arbitrary numbers 312, 266, 110 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.