Highest Common Factor of 640, 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, 460 i.e. 20 the largest integer that leaves a remainder zero for all numbers.
HCF of 640, 460 is 20 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, 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, 460 is 20.
HCF(640, 460) = 20
HCF of 640, 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, 460 is 20.
Highest Common Factor of 640,460 is 20
Step 1: Since 640 > 460, we apply the division lemma to 640 and 460, to get
640 = 460 x 1 + 180
Step 2: Since the reminder 460 ≠ 0, we apply division lemma to 180 and 460, to get
460 = 180 x 2 + 100
Step 3: We consider the new divisor 180 and the new remainder 100, and apply the division lemma to get
180 = 100 x 1 + 80
We consider the new divisor 100 and the new remainder 80,and apply the division lemma to get
100 = 80 x 1 + 20
We consider the new divisor 80 and the new remainder 20,and apply the division lemma to get
80 = 20 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 640 and 460 is 20
Notice that 20 = HCF(80,20) = HCF(100,80) = HCF(180,100) = HCF(460,180) = HCF(640,460) .
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Frequently Asked Questions on HCF of 640, 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, 460?
Answer: HCF of 640, 460 is 20 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 640, 460 using Euclid's Algorithm?
Answer: For arbitrary numbers 640, 460 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.