Highest Common Factor of 2115, 9909 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 2115, 9909 i.e. 9 the largest integer that leaves a remainder zero for all numbers.
HCF of 2115, 9909 is 9 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 2115, 9909 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 2115, 9909 is 9.
HCF(2115, 9909) = 9
HCF of 2115, 9909 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2115, 9909 is 9.
Highest Common Factor of 2115,9909 is 9
Step 1: Since 9909 > 2115, we apply the division lemma to 9909 and 2115, to get
9909 = 2115 x 4 + 1449
Step 2: Since the reminder 2115 ≠ 0, we apply division lemma to 1449 and 2115, to get
2115 = 1449 x 1 + 666
Step 3: We consider the new divisor 1449 and the new remainder 666, and apply the division lemma to get
1449 = 666 x 2 + 117
We consider the new divisor 666 and the new remainder 117,and apply the division lemma to get
666 = 117 x 5 + 81
We consider the new divisor 117 and the new remainder 81,and apply the division lemma to get
117 = 81 x 1 + 36
We consider the new divisor 81 and the new remainder 36,and apply the division lemma to get
81 = 36 x 2 + 9
We consider the new divisor 36 and the new remainder 9,and apply the division lemma to get
36 = 9 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 2115 and 9909 is 9
Notice that 9 = HCF(36,9) = HCF(81,36) = HCF(117,81) = HCF(666,117) = HCF(1449,666) = HCF(2115,1449) = HCF(9909,2115) .
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Frequently Asked Questions on HCF of 2115, 9909 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 2115, 9909?
Answer: HCF of 2115, 9909 is 9 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2115, 9909 using Euclid's Algorithm?
Answer: For arbitrary numbers 2115, 9909 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.