Highest Common Factor of 453, 309, 459 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, 309, 459 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 453, 309, 459 is 3 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, 309, 459 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, 309, 459 is 3.
HCF(453, 309, 459) = 3
HCF of 453, 309, 459 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 453, 309, 459 is 3.
Highest Common Factor of 453,309,459 is 3
Step 1: Since 453 > 309, we apply the division lemma to 453 and 309, to get
453 = 309 x 1 + 144
Step 2: Since the reminder 309 ≠ 0, we apply division lemma to 144 and 309, to get
309 = 144 x 2 + 21
Step 3: We consider the new divisor 144 and the new remainder 21, and apply the division lemma to get
144 = 21 x 6 + 18
We consider the new divisor 21 and the new remainder 18,and apply the division lemma to get
21 = 18 x 1 + 3
We consider the new divisor 18 and the new remainder 3,and apply the division lemma to get
18 = 3 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 453 and 309 is 3
Notice that 3 = HCF(18,3) = HCF(21,18) = HCF(144,21) = HCF(309,144) = HCF(453,309) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 459 > 3, we apply the division lemma to 459 and 3, to get
459 = 3 x 153 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 459 is 3
Notice that 3 = HCF(459,3) .
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, 309, 459 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, 309, 459?
Answer: HCF of 453, 309, 459 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 453, 309, 459 using Euclid's Algorithm?
Answer: For arbitrary numbers 453, 309, 459 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.