Highest Common Factor of 661, 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 661, 465 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 661, 465 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, 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 661, 465 is 1.
HCF(661, 465) = 1
HCF of 661, 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 661, 465 is 1.
Highest Common Factor of 661,465 is 1
Step 1: Since 661 > 465, we apply the division lemma to 661 and 465, to get
661 = 465 x 1 + 196
Step 2: Since the reminder 465 ≠ 0, we apply division lemma to 196 and 465, to get
465 = 196 x 2 + 73
Step 3: We consider the new divisor 196 and the new remainder 73, and apply the division lemma to get
196 = 73 x 2 + 50
We consider the new divisor 73 and the new remainder 50,and apply the division lemma to get
73 = 50 x 1 + 23
We consider the new divisor 50 and the new remainder 23,and apply the division lemma to get
50 = 23 x 2 + 4
We consider the new divisor 23 and the new remainder 4,and apply the division lemma to get
23 = 4 x 5 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 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 465 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(23,4) = HCF(50,23) = HCF(73,50) = HCF(196,73) = HCF(465,196) = HCF(661,465) .
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, 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 661, 465?
Answer: HCF of 661, 465 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 661, 465 using Euclid's Algorithm?
Answer: For arbitrary numbers 661, 465 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
