Highest Common Factor of 725, 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 725, 560 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 725, 560 is 5 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 725, 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 725, 560 is 5.
HCF(725, 560) = 5
HCF of 725, 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 725, 560 is 5.
Highest Common Factor of 725,560 is 5
Step 1: Since 725 > 560, we apply the division lemma to 725 and 560, to get
725 = 560 x 1 + 165
Step 2: Since the reminder 560 ≠ 0, we apply division lemma to 165 and 560, to get
560 = 165 x 3 + 65
Step 3: We consider the new divisor 165 and the new remainder 65, and apply the division lemma to get
165 = 65 x 2 + 35
We consider the new divisor 65 and the new remainder 35,and apply the division lemma to get
65 = 35 x 1 + 30
We consider the new divisor 35 and the new remainder 30,and apply the division lemma to get
35 = 30 x 1 + 5
We consider the new divisor 30 and the new remainder 5,and apply the division lemma to get
30 = 5 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 725 and 560 is 5
Notice that 5 = HCF(30,5) = HCF(35,30) = HCF(65,35) = HCF(165,65) = HCF(560,165) = HCF(725,560) .
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Frequently Asked Questions on HCF of 725, 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 725, 560?
Answer: HCF of 725, 560 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 725, 560 using Euclid's Algorithm?
Answer: For arbitrary numbers 725, 560 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.