Highest Common Factor of 861, 664, 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 861, 664, 227 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 861, 664, 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 861, 664, 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 861, 664, 227 is 1.
HCF(861, 664, 227) = 1
HCF of 861, 664, 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 861, 664, 227 is 1.
Highest Common Factor of 861,664,227 is 1
Step 1: Since 861 > 664, we apply the division lemma to 861 and 664, to get
861 = 664 x 1 + 197
Step 2: Since the reminder 664 ≠ 0, we apply division lemma to 197 and 664, to get
664 = 197 x 3 + 73
Step 3: We consider the new divisor 197 and the new remainder 73, and apply the division lemma to get
197 = 73 x 2 + 51
We consider the new divisor 73 and the new remainder 51,and apply the division lemma to get
73 = 51 x 1 + 22
We consider the new divisor 51 and the new remainder 22,and apply the division lemma to get
51 = 22 x 2 + 7
We consider the new divisor 22 and the new remainder 7,and apply the division lemma to get
22 = 7 x 3 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 861 and 664 is 1
Notice that 1 = HCF(7,1) = HCF(22,7) = HCF(51,22) = HCF(73,51) = HCF(197,73) = HCF(664,197) = HCF(861,664) .
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) .
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Frequently Asked Questions on HCF of 861, 664, 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 861, 664, 227?
Answer: HCF of 861, 664, 227 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 861, 664, 227 using Euclid's Algorithm?
Answer: For arbitrary numbers 861, 664, 227 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.