Highest Common Factor of 665, 258, 214 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 665, 258, 214 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 665, 258, 214 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 665, 258, 214 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 665, 258, 214 is 1.

HCF(665, 258, 214) = 1

HCF of 665, 258, 214 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 665, 258, 214 is 1.

Highest Common Factor of 665,258,214 using Euclid's algorithm

Highest Common Factor of 665,258,214 is 1

Step 1: Since 665 > 258, we apply the division lemma to 665 and 258, to get

665 = 258 x 2 + 149

Step 2: Since the reminder 258 ≠ 0, we apply division lemma to 149 and 258, to get

258 = 149 x 1 + 109

Step 3: We consider the new divisor 149 and the new remainder 109, and apply the division lemma to get

149 = 109 x 1 + 40

We consider the new divisor 109 and the new remainder 40,and apply the division lemma to get

109 = 40 x 2 + 29

We consider the new divisor 40 and the new remainder 29,and apply the division lemma to get

40 = 29 x 1 + 11

We consider the new divisor 29 and the new remainder 11,and apply the division lemma to get

29 = 11 x 2 + 7

We consider the new divisor 11 and the new remainder 7,and apply the division lemma to get

11 = 7 x 1 + 4

We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get

7 = 4 x 1 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 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 665 and 258 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(11,7) = HCF(29,11) = HCF(40,29) = HCF(109,40) = HCF(149,109) = HCF(258,149) = HCF(665,258) .

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

Step 1: Since 214 > 1, we apply the division lemma to 214 and 1, to get

214 = 1 x 214 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 214 is 1

Notice that 1 = HCF(214,1) .

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Frequently Asked Questions on HCF of 665, 258, 214 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 665, 258, 214?

Answer: HCF of 665, 258, 214 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 665, 258, 214 using Euclid's Algorithm?

Answer: For arbitrary numbers 665, 258, 214 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.