Highest Common Factor of 640, 350, 460 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 640, 350, 460 i.e. 10 the largest integer that leaves a remainder zero for all numbers.
HCF of 640, 350, 460 is 10 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 640, 350, 460 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 640, 350, 460 is 10.
HCF(640, 350, 460) = 10
HCF of 640, 350, 460 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 640, 350, 460 is 10.
Highest Common Factor of 640,350,460 is 10
Step 1: Since 640 > 350, we apply the division lemma to 640 and 350, to get
640 = 350 x 1 + 290
Step 2: Since the reminder 350 ≠ 0, we apply division lemma to 290 and 350, to get
350 = 290 x 1 + 60
Step 3: We consider the new divisor 290 and the new remainder 60, and apply the division lemma to get
290 = 60 x 4 + 50
We consider the new divisor 60 and the new remainder 50,and apply the division lemma to get
60 = 50 x 1 + 10
We consider the new divisor 50 and the new remainder 10,and apply the division lemma to get
50 = 10 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 640 and 350 is 10
Notice that 10 = HCF(50,10) = HCF(60,50) = HCF(290,60) = HCF(350,290) = HCF(640,350) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 460 > 10, we apply the division lemma to 460 and 10, to get
460 = 10 x 46 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 10 and 460 is 10
Notice that 10 = HCF(460,10) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 640, 350, 460 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 640, 350, 460?
Answer: HCF of 640, 350, 460 is 10 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 640, 350, 460 using Euclid's Algorithm?
Answer: For arbitrary numbers 640, 350, 460 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.