Highest Common Factor of 614, 753, 450 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 614, 753, 450 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 614, 753, 450 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 614, 753, 450 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 614, 753, 450 is 1.

HCF(614, 753, 450) = 1

HCF of 614, 753, 450 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 614, 753, 450 is 1.

Highest Common Factor of 614,753,450 using Euclid's algorithm

Highest Common Factor of 614,753,450 is 1

Step 1: Since 753 > 614, we apply the division lemma to 753 and 614, to get

753 = 614 x 1 + 139

Step 2: Since the reminder 614 ≠ 0, we apply division lemma to 139 and 614, to get

614 = 139 x 4 + 58

Step 3: We consider the new divisor 139 and the new remainder 58, and apply the division lemma to get

139 = 58 x 2 + 23

We consider the new divisor 58 and the new remainder 23,and apply the division lemma to get

58 = 23 x 2 + 12

We consider the new divisor 23 and the new remainder 12,and apply the division lemma to get

23 = 12 x 1 + 11

We consider the new divisor 12 and the new remainder 11,and apply the division lemma to get

12 = 11 x 1 + 1

We consider the new divisor 11 and the new remainder 1,and apply the division lemma to get

11 = 1 x 11 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 614 and 753 is 1

Notice that 1 = HCF(11,1) = HCF(12,11) = HCF(23,12) = HCF(58,23) = HCF(139,58) = HCF(614,139) = HCF(753,614) .

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

Step 1: Since 450 > 1, we apply the division lemma to 450 and 1, to get

450 = 1 x 450 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 450 is 1

Notice that 1 = HCF(450,1) .

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Frequently Asked Questions on HCF of 614, 753, 450 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 614, 753, 450?

Answer: HCF of 614, 753, 450 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 614, 753, 450 using Euclid's Algorithm?

Answer: For arbitrary numbers 614, 753, 450 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.