Highest Common Factor of 8760, 2585 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 8760, 2585 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 8760, 2585 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 8760, 2585 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 8760, 2585 is 5.
HCF(8760, 2585) = 5
HCF of 8760, 2585 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8760, 2585 is 5.
Highest Common Factor of 8760,2585 is 5
Step 1: Since 8760 > 2585, we apply the division lemma to 8760 and 2585, to get
8760 = 2585 x 3 + 1005
Step 2: Since the reminder 2585 ≠ 0, we apply division lemma to 1005 and 2585, to get
2585 = 1005 x 2 + 575
Step 3: We consider the new divisor 1005 and the new remainder 575, and apply the division lemma to get
1005 = 575 x 1 + 430
We consider the new divisor 575 and the new remainder 430,and apply the division lemma to get
575 = 430 x 1 + 145
We consider the new divisor 430 and the new remainder 145,and apply the division lemma to get
430 = 145 x 2 + 140
We consider the new divisor 145 and the new remainder 140,and apply the division lemma to get
145 = 140 x 1 + 5
We consider the new divisor 140 and the new remainder 5,and apply the division lemma to get
140 = 5 x 28 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 8760 and 2585 is 5
Notice that 5 = HCF(140,5) = HCF(145,140) = HCF(430,145) = HCF(575,430) = HCF(1005,575) = HCF(2585,1005) = HCF(8760,2585) .
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Frequently Asked Questions on HCF of 8760, 2585 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 8760, 2585?
Answer: HCF of 8760, 2585 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8760, 2585 using Euclid's Algorithm?
Answer: For arbitrary numbers 8760, 2585 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.