Highest Common Factor of 8565, 5205 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 8565, 5205 i.e. 15 the largest integer that leaves a remainder zero for all numbers.
HCF of 8565, 5205 is 15 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 8565, 5205 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 8565, 5205 is 15.
HCF(8565, 5205) = 15
HCF of 8565, 5205 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8565, 5205 is 15.
Highest Common Factor of 8565,5205 is 15
Step 1: Since 8565 > 5205, we apply the division lemma to 8565 and 5205, to get
8565 = 5205 x 1 + 3360
Step 2: Since the reminder 5205 ≠ 0, we apply division lemma to 3360 and 5205, to get
5205 = 3360 x 1 + 1845
Step 3: We consider the new divisor 3360 and the new remainder 1845, and apply the division lemma to get
3360 = 1845 x 1 + 1515
We consider the new divisor 1845 and the new remainder 1515,and apply the division lemma to get
1845 = 1515 x 1 + 330
We consider the new divisor 1515 and the new remainder 330,and apply the division lemma to get
1515 = 330 x 4 + 195
We consider the new divisor 330 and the new remainder 195,and apply the division lemma to get
330 = 195 x 1 + 135
We consider the new divisor 195 and the new remainder 135,and apply the division lemma to get
195 = 135 x 1 + 60
We consider the new divisor 135 and the new remainder 60,and apply the division lemma to get
135 = 60 x 2 + 15
We consider the new divisor 60 and the new remainder 15,and apply the division lemma to get
60 = 15 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 8565 and 5205 is 15
Notice that 15 = HCF(60,15) = HCF(135,60) = HCF(195,135) = HCF(330,195) = HCF(1515,330) = HCF(1845,1515) = HCF(3360,1845) = HCF(5205,3360) = HCF(8565,5205) .
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Frequently Asked Questions on HCF of 8565, 5205 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 8565, 5205?
Answer: HCF of 8565, 5205 is 15 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8565, 5205 using Euclid's Algorithm?
Answer: For arbitrary numbers 8565, 5205 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.