Highest Common Factor of 459, 2475 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 459, 2475 i.e. 9 the largest integer that leaves a remainder zero for all numbers.
HCF of 459, 2475 is 9 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 459, 2475 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 459, 2475 is 9.
HCF(459, 2475) = 9
HCF of 459, 2475 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 459, 2475 is 9.
Highest Common Factor of 459,2475 is 9
Step 1: Since 2475 > 459, we apply the division lemma to 2475 and 459, to get
2475 = 459 x 5 + 180
Step 2: Since the reminder 459 ≠ 0, we apply division lemma to 180 and 459, to get
459 = 180 x 2 + 99
Step 3: We consider the new divisor 180 and the new remainder 99, and apply the division lemma to get
180 = 99 x 1 + 81
We consider the new divisor 99 and the new remainder 81,and apply the division lemma to get
99 = 81 x 1 + 18
We consider the new divisor 81 and the new remainder 18,and apply the division lemma to get
81 = 18 x 4 + 9
We consider the new divisor 18 and the new remainder 9,and apply the division lemma to get
18 = 9 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 459 and 2475 is 9
Notice that 9 = HCF(18,9) = HCF(81,18) = HCF(99,81) = HCF(180,99) = HCF(459,180) = HCF(2475,459) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 459, 2475 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 459, 2475?
Answer: HCF of 459, 2475 is 9 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 459, 2475 using Euclid's Algorithm?
Answer: For arbitrary numbers 459, 2475 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.