Highest Common Factor of 714, 441, 659 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 714, 441, 659 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 714, 441, 659 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 714, 441, 659 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 714, 441, 659 is 1.

HCF(714, 441, 659) = 1

HCF of 714, 441, 659 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 714, 441, 659 is 1.

Highest Common Factor of 714,441,659 using Euclid's algorithm

Highest Common Factor of 714,441,659 is 1

Step 1: Since 714 > 441, we apply the division lemma to 714 and 441, to get

714 = 441 x 1 + 273

Step 2: Since the reminder 441 ≠ 0, we apply division lemma to 273 and 441, to get

441 = 273 x 1 + 168

Step 3: We consider the new divisor 273 and the new remainder 168, and apply the division lemma to get

273 = 168 x 1 + 105

We consider the new divisor 168 and the new remainder 105,and apply the division lemma to get

168 = 105 x 1 + 63

We consider the new divisor 105 and the new remainder 63,and apply the division lemma to get

105 = 63 x 1 + 42

We consider the new divisor 63 and the new remainder 42,and apply the division lemma to get

63 = 42 x 1 + 21

We consider the new divisor 42 and the new remainder 21,and apply the division lemma to get

42 = 21 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 21, the HCF of 714 and 441 is 21

Notice that 21 = HCF(42,21) = HCF(63,42) = HCF(105,63) = HCF(168,105) = HCF(273,168) = HCF(441,273) = HCF(714,441) .

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

Step 1: Since 659 > 21, we apply the division lemma to 659 and 21, to get

659 = 21 x 31 + 8

Step 2: Since the reminder 21 ≠ 0, we apply division lemma to 8 and 21, to get

21 = 8 x 2 + 5

Step 3: We consider the new divisor 8 and the new remainder 5, and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 21 and 659 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(21,8) = HCF(659,21) .

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Frequently Asked Questions on HCF of 714, 441, 659 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 714, 441, 659?

Answer: HCF of 714, 441, 659 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 714, 441, 659 using Euclid's Algorithm?

Answer: For arbitrary numbers 714, 441, 659 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.