Highest Common Factor of 6005, 2078 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 6005, 2078 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 6005, 2078 is 1 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 6005, 2078 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 6005, 2078 is 1.
HCF(6005, 2078) = 1
HCF of 6005, 2078 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6005, 2078 is 1.
Highest Common Factor of 6005,2078 is 1
Step 1: Since 6005 > 2078, we apply the division lemma to 6005 and 2078, to get
6005 = 2078 x 2 + 1849
Step 2: Since the reminder 2078 ≠ 0, we apply division lemma to 1849 and 2078, to get
2078 = 1849 x 1 + 229
Step 3: We consider the new divisor 1849 and the new remainder 229, and apply the division lemma to get
1849 = 229 x 8 + 17
We consider the new divisor 229 and the new remainder 17,and apply the division lemma to get
229 = 17 x 13 + 8
We consider the new divisor 17 and the new remainder 8,and apply the division lemma to get
17 = 8 x 2 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6005 and 2078 is 1
Notice that 1 = HCF(8,1) = HCF(17,8) = HCF(229,17) = HCF(1849,229) = HCF(2078,1849) = HCF(6005,2078) .
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Frequently Asked Questions on HCF of 6005, 2078 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 6005, 2078?
Answer: HCF of 6005, 2078 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6005, 2078 using Euclid's Algorithm?
Answer: For arbitrary numbers 6005, 2078 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.