Highest Common Factor of 2125, 8665 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 2125, 8665 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 2125, 8665 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 2125, 8665 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 2125, 8665 is 5.
HCF(2125, 8665) = 5
HCF of 2125, 8665 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2125, 8665 is 5.
Highest Common Factor of 2125,8665 is 5
Step 1: Since 8665 > 2125, we apply the division lemma to 8665 and 2125, to get
8665 = 2125 x 4 + 165
Step 2: Since the reminder 2125 ≠ 0, we apply division lemma to 165 and 2125, to get
2125 = 165 x 12 + 145
Step 3: We consider the new divisor 165 and the new remainder 145, and apply the division lemma to get
165 = 145 x 1 + 20
We consider the new divisor 145 and the new remainder 20,and apply the division lemma to get
145 = 20 x 7 + 5
We consider the new divisor 20 and the new remainder 5,and apply the division lemma to get
20 = 5 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 2125 and 8665 is 5
Notice that 5 = HCF(20,5) = HCF(145,20) = HCF(165,145) = HCF(2125,165) = HCF(8665,2125) .
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Frequently Asked Questions on HCF of 2125, 8665 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 2125, 8665?
Answer: HCF of 2125, 8665 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2125, 8665 using Euclid's Algorithm?
Answer: For arbitrary numbers 2125, 8665 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.