Highest Common Factor of 300, 2219, 7981 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 300, 2219, 7981 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 300, 2219, 7981 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 300, 2219, 7981 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 300, 2219, 7981 is 1.

HCF(300, 2219, 7981) = 1

HCF of 300, 2219, 7981 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 300, 2219, 7981 is 1.

Highest Common Factor of 300,2219,7981 using Euclid's algorithm

Highest Common Factor of 300,2219,7981 is 1

Step 1: Since 2219 > 300, we apply the division lemma to 2219 and 300, to get

2219 = 300 x 7 + 119

Step 2: Since the reminder 300 ≠ 0, we apply division lemma to 119 and 300, to get

300 = 119 x 2 + 62

Step 3: We consider the new divisor 119 and the new remainder 62, and apply the division lemma to get

119 = 62 x 1 + 57

We consider the new divisor 62 and the new remainder 57,and apply the division lemma to get

62 = 57 x 1 + 5

We consider the new divisor 57 and the new remainder 5,and apply the division lemma to get

57 = 5 x 11 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 300 and 2219 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(57,5) = HCF(62,57) = HCF(119,62) = HCF(300,119) = HCF(2219,300) .

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

Step 1: Since 7981 > 1, we apply the division lemma to 7981 and 1, to get

7981 = 1 x 7981 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 7981 is 1

Notice that 1 = HCF(7981,1) .

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Frequently Asked Questions on HCF of 300, 2219, 7981 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 300, 2219, 7981?

Answer: HCF of 300, 2219, 7981 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 300, 2219, 7981 using Euclid's Algorithm?

Answer: For arbitrary numbers 300, 2219, 7981 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.