Highest Common Factor of 453, 702, 965 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 453, 702, 965 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 453, 702, 965 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 453, 702, 965 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 453, 702, 965 is 1.

HCF(453, 702, 965) = 1

HCF of 453, 702, 965 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 453, 702, 965 is 1.

Highest Common Factor of 453,702,965 using Euclid's algorithm

Highest Common Factor of 453,702,965 is 1

Step 1: Since 702 > 453, we apply the division lemma to 702 and 453, to get

702 = 453 x 1 + 249

Step 2: Since the reminder 453 ≠ 0, we apply division lemma to 249 and 453, to get

453 = 249 x 1 + 204

Step 3: We consider the new divisor 249 and the new remainder 204, and apply the division lemma to get

249 = 204 x 1 + 45

We consider the new divisor 204 and the new remainder 45,and apply the division lemma to get

204 = 45 x 4 + 24

We consider the new divisor 45 and the new remainder 24,and apply the division lemma to get

45 = 24 x 1 + 21

We consider the new divisor 24 and the new remainder 21,and apply the division lemma to get

24 = 21 x 1 + 3

We consider the new divisor 21 and the new remainder 3,and apply the division lemma to get

21 = 3 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 453 and 702 is 3

Notice that 3 = HCF(21,3) = HCF(24,21) = HCF(45,24) = HCF(204,45) = HCF(249,204) = HCF(453,249) = HCF(702,453) .

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

Step 1: Since 965 > 3, we apply the division lemma to 965 and 3, to get

965 = 3 x 321 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: 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 3 and 965 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(965,3) .

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Frequently Asked Questions on HCF of 453, 702, 965 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 453, 702, 965?

Answer: HCF of 453, 702, 965 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 453, 702, 965 using Euclid's Algorithm?

Answer: For arbitrary numbers 453, 702, 965 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.