Highest Common Factor of 3755, 2040 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 3755, 2040 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 3755, 2040 is 5 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 3755, 2040 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 3755, 2040 is 5.
HCF(3755, 2040) = 5
HCF of 3755, 2040 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3755, 2040 is 5.
Highest Common Factor of 3755,2040 is 5
Step 1: Since 3755 > 2040, we apply the division lemma to 3755 and 2040, to get
3755 = 2040 x 1 + 1715
Step 2: Since the reminder 2040 ≠ 0, we apply division lemma to 1715 and 2040, to get
2040 = 1715 x 1 + 325
Step 3: We consider the new divisor 1715 and the new remainder 325, and apply the division lemma to get
1715 = 325 x 5 + 90
We consider the new divisor 325 and the new remainder 90,and apply the division lemma to get
325 = 90 x 3 + 55
We consider the new divisor 90 and the new remainder 55,and apply the division lemma to get
90 = 55 x 1 + 35
We consider the new divisor 55 and the new remainder 35,and apply the division lemma to get
55 = 35 x 1 + 20
We consider the new divisor 35 and the new remainder 20,and apply the division lemma to get
35 = 20 x 1 + 15
We consider the new divisor 20 and the new remainder 15,and apply the division lemma to get
20 = 15 x 1 + 5
We consider the new divisor 15 and the new remainder 5,and apply the division lemma to get
15 = 5 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 3755 and 2040 is 5
Notice that 5 = HCF(15,5) = HCF(20,15) = HCF(35,20) = HCF(55,35) = HCF(90,55) = HCF(325,90) = HCF(1715,325) = HCF(2040,1715) = HCF(3755,2040) .
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Frequently Asked Questions on HCF of 3755, 2040 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 3755, 2040?
Answer: HCF of 3755, 2040 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3755, 2040 using Euclid's Algorithm?
Answer: For arbitrary numbers 3755, 2040 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.