Highest Common Factor of 399, 709, 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 399, 709, 218 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 399, 709, 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 399, 709, 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 399, 709, 218 is 1.

HCF(399, 709, 218) = 1

HCF of 399, 709, 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 399, 709, 218 is 1.

Highest Common Factor of 399,709,218 using Euclid's algorithm

Highest Common Factor of 399,709,218 is 1

Step 1: Since 709 > 399, we apply the division lemma to 709 and 399, to get

709 = 399 x 1 + 310

Step 2: Since the reminder 399 ≠ 0, we apply division lemma to 310 and 399, to get

399 = 310 x 1 + 89

Step 3: We consider the new divisor 310 and the new remainder 89, and apply the division lemma to get

310 = 89 x 3 + 43

We consider the new divisor 89 and the new remainder 43,and apply the division lemma to get

89 = 43 x 2 + 3

We consider the new divisor 43 and the new remainder 3,and apply the division lemma to get

43 = 3 x 14 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 399 and 709 is 1

Notice that 1 = HCF(3,1) = HCF(43,3) = HCF(89,43) = HCF(310,89) = HCF(399,310) = HCF(709,399) .

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

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

218 = 1 x 218 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 218 is 1

Notice that 1 = HCF(218,1) .

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Frequently Asked Questions on HCF of 399, 709, 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 399, 709, 218?

Answer: HCF of 399, 709, 218 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 399, 709, 218 using Euclid's Algorithm?

Answer: For arbitrary numbers 399, 709, 218 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.