Highest Common Factor of 460, 646, 606 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 460, 646, 606 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 460, 646, 606 is 2 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 460, 646, 606 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 460, 646, 606 is 2.
HCF(460, 646, 606) = 2
HCF of 460, 646, 606 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 460, 646, 606 is 2.
Highest Common Factor of 460,646,606 is 2
Step 1: Since 646 > 460, we apply the division lemma to 646 and 460, to get
646 = 460 x 1 + 186
Step 2: Since the reminder 460 ≠ 0, we apply division lemma to 186 and 460, to get
460 = 186 x 2 + 88
Step 3: We consider the new divisor 186 and the new remainder 88, and apply the division lemma to get
186 = 88 x 2 + 10
We consider the new divisor 88 and the new remainder 10,and apply the division lemma to get
88 = 10 x 8 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 460 and 646 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(88,10) = HCF(186,88) = HCF(460,186) = HCF(646,460) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 606 > 2, we apply the division lemma to 606 and 2, to get
606 = 2 x 303 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 606 is 2
Notice that 2 = HCF(606,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 460, 646, 606 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 460, 646, 606?
Answer: HCF of 460, 646, 606 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 460, 646, 606 using Euclid's Algorithm?
Answer: For arbitrary numbers 460, 646, 606 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.