Highest Common Factor of 7405, 5180, 65660 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 7405, 5180, 65660 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 7405, 5180, 65660 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 7405, 5180, 65660 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 7405, 5180, 65660 is 5.
HCF(7405, 5180, 65660) = 5
HCF of 7405, 5180, 65660 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7405, 5180, 65660 is 5.
Highest Common Factor of 7405,5180,65660 is 5
Step 1: Since 7405 > 5180, we apply the division lemma to 7405 and 5180, to get
7405 = 5180 x 1 + 2225
Step 2: Since the reminder 5180 ≠ 0, we apply division lemma to 2225 and 5180, to get
5180 = 2225 x 2 + 730
Step 3: We consider the new divisor 2225 and the new remainder 730, and apply the division lemma to get
2225 = 730 x 3 + 35
We consider the new divisor 730 and the new remainder 35,and apply the division lemma to get
730 = 35 x 20 + 30
We consider the new divisor 35 and the new remainder 30,and apply the division lemma to get
35 = 30 x 1 + 5
We consider the new divisor 30 and the new remainder 5,and apply the division lemma to get
30 = 5 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 7405 and 5180 is 5
Notice that 5 = HCF(30,5) = HCF(35,30) = HCF(730,35) = HCF(2225,730) = HCF(5180,2225) = HCF(7405,5180) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 65660 > 5, we apply the division lemma to 65660 and 5, to get
65660 = 5 x 13132 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5 and 65660 is 5
Notice that 5 = HCF(65660,5) .
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Frequently Asked Questions on HCF of 7405, 5180, 65660 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 7405, 5180, 65660?
Answer: HCF of 7405, 5180, 65660 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7405, 5180, 65660 using Euclid's Algorithm?
Answer: For arbitrary numbers 7405, 5180, 65660 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.