Highest Common Factor of 6105, 2067 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 6105, 2067 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 6105, 2067 is 3 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 6105, 2067 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 6105, 2067 is 3.
HCF(6105, 2067) = 3
HCF of 6105, 2067 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6105, 2067 is 3.
Highest Common Factor of 6105,2067 is 3
Step 1: Since 6105 > 2067, we apply the division lemma to 6105 and 2067, to get
6105 = 2067 x 2 + 1971
Step 2: Since the reminder 2067 ≠ 0, we apply division lemma to 1971 and 2067, to get
2067 = 1971 x 1 + 96
Step 3: We consider the new divisor 1971 and the new remainder 96, and apply the division lemma to get
1971 = 96 x 20 + 51
We consider the new divisor 96 and the new remainder 51,and apply the division lemma to get
96 = 51 x 1 + 45
We consider the new divisor 51 and the new remainder 45,and apply the division lemma to get
51 = 45 x 1 + 6
We consider the new divisor 45 and the new remainder 6,and apply the division lemma to get
45 = 6 x 7 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 6105 and 2067 is 3
Notice that 3 = HCF(6,3) = HCF(45,6) = HCF(51,45) = HCF(96,51) = HCF(1971,96) = HCF(2067,1971) = HCF(6105,2067) .
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Frequently Asked Questions on HCF of 6105, 2067 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 6105, 2067?
Answer: HCF of 6105, 2067 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6105, 2067 using Euclid's Algorithm?
Answer: For arbitrary numbers 6105, 2067 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.