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 500, 905, 461 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 500, 905, 461 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 500, 905, 461 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 500, 905, 461 is 1.
HCF(500, 905, 461) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 500, 905, 461 is 1.
Step 1: Since 905 > 500, we apply the division lemma to 905 and 500, to get
905 = 500 x 1 + 405
Step 2: Since the reminder 500 ≠ 0, we apply division lemma to 405 and 500, to get
500 = 405 x 1 + 95
Step 3: We consider the new divisor 405 and the new remainder 95, and apply the division lemma to get
405 = 95 x 4 + 25
We consider the new divisor 95 and the new remainder 25,and apply the division lemma to get
95 = 25 x 3 + 20
We consider the new divisor 25 and the new remainder 20,and apply the division lemma to get
25 = 20 x 1 + 5
We consider the new divisor 20 and the new remainder 5,and apply the division lemma to get
20 = 5 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 500 and 905 is 5
Notice that 5 = HCF(20,5) = HCF(25,20) = HCF(95,25) = HCF(405,95) = HCF(500,405) = HCF(905,500) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 461 > 5, we apply the division lemma to 461 and 5, to get
461 = 5 x 92 + 1
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 1 and 5, to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 461 is 1
Notice that 1 = HCF(5,1) = HCF(461,5) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 500, 905, 461?
Answer: HCF of 500, 905, 461 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 500, 905, 461 using Euclid's Algorithm?
Answer: For arbitrary numbers 500, 905, 461 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.