Highest Common Factor of 8005, 9660 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 8005, 9660 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 8005, 9660 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 8005, 9660 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 8005, 9660 is 5.
HCF(8005, 9660) = 5
HCF of 8005, 9660 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8005, 9660 is 5.
Highest Common Factor of 8005,9660 is 5
Step 1: Since 9660 > 8005, we apply the division lemma to 9660 and 8005, to get
9660 = 8005 x 1 + 1655
Step 2: Since the reminder 8005 ≠ 0, we apply division lemma to 1655 and 8005, to get
8005 = 1655 x 4 + 1385
Step 3: We consider the new divisor 1655 and the new remainder 1385, and apply the division lemma to get
1655 = 1385 x 1 + 270
We consider the new divisor 1385 and the new remainder 270,and apply the division lemma to get
1385 = 270 x 5 + 35
We consider the new divisor 270 and the new remainder 35,and apply the division lemma to get
270 = 35 x 7 + 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 8005 and 9660 is 5
Notice that 5 = HCF(10,5) = HCF(25,10) = HCF(35,25) = HCF(270,35) = HCF(1385,270) = HCF(1655,1385) = HCF(8005,1655) = HCF(9660,8005) .
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Frequently Asked Questions on HCF of 8005, 9660 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 8005, 9660?
Answer: HCF of 8005, 9660 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8005, 9660 using Euclid's Algorithm?
Answer: For arbitrary numbers 8005, 9660 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.