Highest Common Factor of 460, 560 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, 560 i.e. 20 the largest integer that leaves a remainder zero for all numbers.
HCF of 460, 560 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 460, 560 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, 560 is 20.
HCF(460, 560) = 20
HCF of 460, 560 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, 560 is 20.
Highest Common Factor of 460,560 is 20
Step 1: Since 560 > 460, we apply the division lemma to 560 and 460, to get
560 = 460 x 1 + 100
Step 2: Since the reminder 460 ≠ 0, we apply division lemma to 100 and 460, to get
460 = 100 x 4 + 60
Step 3: We consider the new divisor 100 and the new remainder 60, and apply the division lemma to get
100 = 60 x 1 + 40
We consider the new divisor 60 and the new remainder 40,and apply the division lemma to get
60 = 40 x 1 + 20
We consider the new divisor 40 and the new remainder 20,and apply the division lemma to get
40 = 20 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 460 and 560 is 20
Notice that 20 = HCF(40,20) = HCF(60,40) = HCF(100,60) = HCF(460,100) = HCF(560,460) .
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Frequently Asked Questions on HCF of 460, 560 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, 560?
Answer: HCF of 460, 560 is 20 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 460, 560 using Euclid's Algorithm?
Answer: For arbitrary numbers 460, 560 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.