Highest Common Factor of 661, 461, 227 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 661, 461, 227 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 661, 461, 227 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 661, 461, 227 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 661, 461, 227 is 1.
HCF(661, 461, 227) = 1
HCF of 661, 461, 227 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 661, 461, 227 is 1.
Highest Common Factor of 661,461,227 is 1
Step 1: Since 661 > 461, we apply the division lemma to 661 and 461, to get
661 = 461 x 1 + 200
Step 2: Since the reminder 461 ≠ 0, we apply division lemma to 200 and 461, to get
461 = 200 x 2 + 61
Step 3: We consider the new divisor 200 and the new remainder 61, and apply the division lemma to get
200 = 61 x 3 + 17
We consider the new divisor 61 and the new remainder 17,and apply the division lemma to get
61 = 17 x 3 + 10
We consider the new divisor 17 and the new remainder 10,and apply the division lemma to get
17 = 10 x 1 + 7
We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get
10 = 7 x 1 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma 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 661 and 461 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(17,10) = HCF(61,17) = HCF(200,61) = HCF(461,200) = HCF(661,461) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 227 > 1, we apply the division lemma to 227 and 1, to get
227 = 1 x 227 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 227 is 1
Notice that 1 = HCF(227,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 661, 461, 227 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 661, 461, 227?
Answer: HCF of 661, 461, 227 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 661, 461, 227 using Euclid's Algorithm?
Answer: For arbitrary numbers 661, 461, 227 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.