Highest Common Factor of 365, 665 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 365, 665 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 365, 665 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 365, 665 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 365, 665 is 5.
HCF(365, 665) = 5
HCF of 365, 665 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 365, 665 is 5.
Highest Common Factor of 365,665 is 5
Step 1: Since 665 > 365, we apply the division lemma to 665 and 365, to get
665 = 365 x 1 + 300
Step 2: Since the reminder 365 ≠ 0, we apply division lemma to 300 and 365, to get
365 = 300 x 1 + 65
Step 3: We consider the new divisor 300 and the new remainder 65, and apply the division lemma to get
300 = 65 x 4 + 40
We consider the new divisor 65 and the new remainder 40,and apply the division lemma to get
65 = 40 x 1 + 25
We consider the new divisor 40 and the new remainder 25,and apply the division lemma to get
40 = 25 x 1 + 15
We consider the new divisor 25 and the new remainder 15,and apply the division lemma to get
25 = 15 x 1 + 10
We consider the new divisor 15 and the new remainder 10,and apply the division lemma to get
15 = 10 x 1 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 365 and 665 is 5
Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(25,15) = HCF(40,25) = HCF(65,40) = HCF(300,65) = HCF(365,300) = HCF(665,365) .
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Frequently Asked Questions on HCF of 365, 665 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 365, 665?
Answer: HCF of 365, 665 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 365, 665 using Euclid's Algorithm?
Answer: For arbitrary numbers 365, 665 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
