Highest Common Factor of 719, 986, 54 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 719, 986, 54 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 719, 986, 54 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 719, 986, 54 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 719, 986, 54 is 1.

HCF(719, 986, 54) = 1

HCF of 719, 986, 54 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 719, 986, 54 is 1.

Highest Common Factor of 719,986,54 using Euclid's algorithm

Highest Common Factor of 719,986,54 is 1

Step 1: Since 986 > 719, we apply the division lemma to 986 and 719, to get

986 = 719 x 1 + 267

Step 2: Since the reminder 719 ≠ 0, we apply division lemma to 267 and 719, to get

719 = 267 x 2 + 185

Step 3: We consider the new divisor 267 and the new remainder 185, and apply the division lemma to get

267 = 185 x 1 + 82

We consider the new divisor 185 and the new remainder 82,and apply the division lemma to get

185 = 82 x 2 + 21

We consider the new divisor 82 and the new remainder 21,and apply the division lemma to get

82 = 21 x 3 + 19

We consider the new divisor 21 and the new remainder 19,and apply the division lemma to get

21 = 19 x 1 + 2

We consider the new divisor 19 and the new remainder 2,and apply the division lemma to get

19 = 2 x 9 + 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 719 and 986 is 1

Notice that 1 = HCF(2,1) = HCF(19,2) = HCF(21,19) = HCF(82,21) = HCF(185,82) = HCF(267,185) = HCF(719,267) = HCF(986,719) .

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

Step 1: Since 54 > 1, we apply the division lemma to 54 and 1, to get

54 = 1 x 54 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 54 is 1

Notice that 1 = HCF(54,1) .

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Frequently Asked Questions on HCF of 719, 986, 54 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 719, 986, 54?

Answer: HCF of 719, 986, 54 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 719, 986, 54 using Euclid's Algorithm?

Answer: For arbitrary numbers 719, 986, 54 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.