Highest Common Factor of 221, 871, 312 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 221, 871, 312 i.e. 13 the largest integer that leaves a remainder zero for all numbers.

HCF of 221, 871, 312 is 13 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 221, 871, 312 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 221, 871, 312 is 13.

HCF(221, 871, 312) = 13

HCF of 221, 871, 312 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 221, 871, 312 is 13.

Highest Common Factor of 221,871,312 using Euclid's algorithm

Highest Common Factor of 221,871,312 is 13

Step 1: Since 871 > 221, we apply the division lemma to 871 and 221, to get

871 = 221 x 3 + 208

Step 2: Since the reminder 221 ≠ 0, we apply division lemma to 208 and 221, to get

221 = 208 x 1 + 13

Step 3: We consider the new divisor 208 and the new remainder 13, and apply the division lemma to get

208 = 13 x 16 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 221 and 871 is 13

Notice that 13 = HCF(208,13) = HCF(221,208) = HCF(871,221) .

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

Step 1: Since 312 > 13, we apply the division lemma to 312 and 13, to get

312 = 13 x 24 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 13 and 312 is 13

Notice that 13 = HCF(312,13) .

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Frequently Asked Questions on HCF of 221, 871, 312 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 221, 871, 312?

Answer: HCF of 221, 871, 312 is 13 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 221, 871, 312 using Euclid's Algorithm?

Answer: For arbitrary numbers 221, 871, 312 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.