Highest Common Factor of 560, 715 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 560, 715 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 560, 715 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 560, 715 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 560, 715 is 5.
HCF(560, 715) = 5
HCF of 560, 715 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 560, 715 is 5.
Highest Common Factor of 560,715 is 5
Step 1: Since 715 > 560, we apply the division lemma to 715 and 560, to get
715 = 560 x 1 + 155
Step 2: Since the reminder 560 ≠ 0, we apply division lemma to 155 and 560, to get
560 = 155 x 3 + 95
Step 3: We consider the new divisor 155 and the new remainder 95, and apply the division lemma to get
155 = 95 x 1 + 60
We consider the new divisor 95 and the new remainder 60,and apply the division lemma to get
95 = 60 x 1 + 35
We consider the new divisor 60 and the new remainder 35,and apply the division lemma to get
60 = 35 x 1 + 25
We consider the new divisor 35 and the new remainder 25,and apply the division lemma to get
35 = 25 x 1 + 10
We consider the new divisor 25 and the new remainder 10,and apply the division lemma to get
25 = 10 x 2 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 560 and 715 is 5
Notice that 5 = HCF(10,5) = HCF(25,10) = HCF(35,25) = HCF(60,35) = HCF(95,60) = HCF(155,95) = HCF(560,155) = HCF(715,560) .
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Frequently Asked Questions on HCF of 560, 715 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 560, 715?
Answer: HCF of 560, 715 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 560, 715 using Euclid's Algorithm?
Answer: For arbitrary numbers 560, 715 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.