Highest Common Factor of 807, 981, 218 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 807, 981, 218 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 807, 981, 218 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 807, 981, 218 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 807, 981, 218 is 1.

HCF(807, 981, 218) = 1

HCF of 807, 981, 218 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 807, 981, 218 is 1.

Highest Common Factor of 807,981,218 using Euclid's algorithm

Highest Common Factor of 807,981,218 is 1

Step 1: Since 981 > 807, we apply the division lemma to 981 and 807, to get

981 = 807 x 1 + 174

Step 2: Since the reminder 807 ≠ 0, we apply division lemma to 174 and 807, to get

807 = 174 x 4 + 111

Step 3: We consider the new divisor 174 and the new remainder 111, and apply the division lemma to get

174 = 111 x 1 + 63

We consider the new divisor 111 and the new remainder 63,and apply the division lemma to get

111 = 63 x 1 + 48

We consider the new divisor 63 and the new remainder 48,and apply the division lemma to get

63 = 48 x 1 + 15

We consider the new divisor 48 and the new remainder 15,and apply the division lemma to get

48 = 15 x 3 + 3

We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get

15 = 3 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 807 and 981 is 3

Notice that 3 = HCF(15,3) = HCF(48,15) = HCF(63,48) = HCF(111,63) = HCF(174,111) = HCF(807,174) = HCF(981,807) .

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

Step 1: Since 218 > 3, we apply the division lemma to 218 and 3, to get

218 = 3 x 72 + 2

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

3 = 2 x 1 + 1

Step 3: 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 3 and 218 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(218,3) .

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Frequently Asked Questions on HCF of 807, 981, 218 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 807, 981, 218?

Answer: HCF of 807, 981, 218 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 807, 981, 218 using Euclid's Algorithm?

Answer: For arbitrary numbers 807, 981, 218 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.