Highest Common Factor of 453, 990, 742 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, 990, 742 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 453, 990, 742 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, 990, 742 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, 990, 742 is 1.

HCF(453, 990, 742) = 1

HCF of 453, 990, 742 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, 990, 742 is 1.

Highest Common Factor of 453,990,742 using Euclid's algorithm

Highest Common Factor of 453,990,742 is 1

Step 1: Since 990 > 453, we apply the division lemma to 990 and 453, to get

990 = 453 x 2 + 84

Step 2: Since the reminder 453 ≠ 0, we apply division lemma to 84 and 453, to get

453 = 84 x 5 + 33

Step 3: We consider the new divisor 84 and the new remainder 33, and apply the division lemma to get

84 = 33 x 2 + 18

We consider the new divisor 33 and the new remainder 18,and apply the division lemma to get

33 = 18 x 1 + 15

We consider the new divisor 18 and the new remainder 15,and apply the division lemma to get

18 = 15 x 1 + 3

We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get

15 = 3 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 453 and 990 is 3

Notice that 3 = HCF(15,3) = HCF(18,15) = HCF(33,18) = HCF(84,33) = HCF(453,84) = HCF(990,453) .

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

Step 1: Since 742 > 3, we apply the division lemma to 742 and 3, to get

742 = 3 x 247 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 742 is 1

Notice that 1 = HCF(3,1) = HCF(742,3) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 453, 990, 742 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, 990, 742?

Answer: HCF of 453, 990, 742 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 453, 990, 742 using Euclid's Algorithm?

Answer: For arbitrary numbers 453, 990, 742 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.