Highest Common Factor of 6645, 9105 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 6645, 9105 i.e. 15 the largest integer that leaves a remainder zero for all numbers.
HCF of 6645, 9105 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 6645, 9105 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 6645, 9105 is 15.
HCF(6645, 9105) = 15
HCF of 6645, 9105 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6645, 9105 is 15.
Highest Common Factor of 6645,9105 is 15
Step 1: Since 9105 > 6645, we apply the division lemma to 9105 and 6645, to get
9105 = 6645 x 1 + 2460
Step 2: Since the reminder 6645 ≠ 0, we apply division lemma to 2460 and 6645, to get
6645 = 2460 x 2 + 1725
Step 3: We consider the new divisor 2460 and the new remainder 1725, and apply the division lemma to get
2460 = 1725 x 1 + 735
We consider the new divisor 1725 and the new remainder 735,and apply the division lemma to get
1725 = 735 x 2 + 255
We consider the new divisor 735 and the new remainder 255,and apply the division lemma to get
735 = 255 x 2 + 225
We consider the new divisor 255 and the new remainder 225,and apply the division lemma to get
255 = 225 x 1 + 30
We consider the new divisor 225 and the new remainder 30,and apply the division lemma to get
225 = 30 x 7 + 15
We consider the new divisor 30 and the new remainder 15,and apply the division lemma to get
30 = 15 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 6645 and 9105 is 15
Notice that 15 = HCF(30,15) = HCF(225,30) = HCF(255,225) = HCF(735,255) = HCF(1725,735) = HCF(2460,1725) = HCF(6645,2460) = HCF(9105,6645) .
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Frequently Asked Questions on HCF of 6645, 9105 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 6645, 9105?
Answer: HCF of 6645, 9105 is 15 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6645, 9105 using Euclid's Algorithm?
Answer: For arbitrary numbers 6645, 9105 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.