Highest Common Factor of 455, 585, 465 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 455, 585, 465 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 455, 585, 465 is 5 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 455, 585, 465 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 455, 585, 465 is 5.
HCF(455, 585, 465) = 5
HCF of 455, 585, 465 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 455, 585, 465 is 5.
Highest Common Factor of 455,585,465 is 5
Step 1: Since 585 > 455, we apply the division lemma to 585 and 455, to get
585 = 455 x 1 + 130
Step 2: Since the reminder 455 ≠ 0, we apply division lemma to 130 and 455, to get
455 = 130 x 3 + 65
Step 3: We consider the new divisor 130 and the new remainder 65, and apply the division lemma to get
130 = 65 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 65, the HCF of 455 and 585 is 65
Notice that 65 = HCF(130,65) = HCF(455,130) = HCF(585,455) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 465 > 65, we apply the division lemma to 465 and 65, to get
465 = 65 x 7 + 10
Step 2: Since the reminder 65 ≠ 0, we apply division lemma to 10 and 65, to get
65 = 10 x 6 + 5
Step 3: We consider the new divisor 10 and the new remainder 5, and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 65 and 465 is 5
Notice that 5 = HCF(10,5) = HCF(65,10) = HCF(465,65) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 455, 585, 465 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 455, 585, 465?
Answer: HCF of 455, 585, 465 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 455, 585, 465 using Euclid's Algorithm?
Answer: For arbitrary numbers 455, 585, 465 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.