Highest Common Factor of 2027, 1305 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 2027, 1305 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2027, 1305 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 2027, 1305 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 2027, 1305 is 1.
HCF(2027, 1305) = 1
HCF of 2027, 1305 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2027, 1305 is 1.
Highest Common Factor of 2027,1305 is 1
Step 1: Since 2027 > 1305, we apply the division lemma to 2027 and 1305, to get
2027 = 1305 x 1 + 722
Step 2: Since the reminder 1305 ≠ 0, we apply division lemma to 722 and 1305, to get
1305 = 722 x 1 + 583
Step 3: We consider the new divisor 722 and the new remainder 583, and apply the division lemma to get
722 = 583 x 1 + 139
We consider the new divisor 583 and the new remainder 139,and apply the division lemma to get
583 = 139 x 4 + 27
We consider the new divisor 139 and the new remainder 27,and apply the division lemma to get
139 = 27 x 5 + 4
We consider the new divisor 27 and the new remainder 4,and apply the division lemma to get
27 = 4 x 6 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2027 and 1305 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(27,4) = HCF(139,27) = HCF(583,139) = HCF(722,583) = HCF(1305,722) = HCF(2027,1305) .
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Frequently Asked Questions on HCF of 2027, 1305 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 2027, 1305?
Answer: HCF of 2027, 1305 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2027, 1305 using Euclid's Algorithm?
Answer: For arbitrary numbers 2027, 1305 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.