Highest Common Factor of 1835, 8515 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 1835, 8515 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 1835, 8515 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 1835, 8515 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 1835, 8515 is 5.
HCF(1835, 8515) = 5
HCF of 1835, 8515 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1835, 8515 is 5.
Highest Common Factor of 1835,8515 is 5
Step 1: Since 8515 > 1835, we apply the division lemma to 8515 and 1835, to get
8515 = 1835 x 4 + 1175
Step 2: Since the reminder 1835 ≠ 0, we apply division lemma to 1175 and 1835, to get
1835 = 1175 x 1 + 660
Step 3: We consider the new divisor 1175 and the new remainder 660, and apply the division lemma to get
1175 = 660 x 1 + 515
We consider the new divisor 660 and the new remainder 515,and apply the division lemma to get
660 = 515 x 1 + 145
We consider the new divisor 515 and the new remainder 145,and apply the division lemma to get
515 = 145 x 3 + 80
We consider the new divisor 145 and the new remainder 80,and apply the division lemma to get
145 = 80 x 1 + 65
We consider the new divisor 80 and the new remainder 65,and apply the division lemma to get
80 = 65 x 1 + 15
We consider the new divisor 65 and the new remainder 15,and apply the division lemma to get
65 = 15 x 4 + 5
We consider the new divisor 15 and the new remainder 5,and apply the division lemma to get
15 = 5 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 1835 and 8515 is 5
Notice that 5 = HCF(15,5) = HCF(65,15) = HCF(80,65) = HCF(145,80) = HCF(515,145) = HCF(660,515) = HCF(1175,660) = HCF(1835,1175) = HCF(8515,1835) .
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Frequently Asked Questions on HCF of 1835, 8515 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 1835, 8515?
Answer: HCF of 1835, 8515 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1835, 8515 using Euclid's Algorithm?
Answer: For arbitrary numbers 1835, 8515 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
