Highest Common Factor of 4005, 320 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 4005, 320 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 4005, 320 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 4005, 320 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 4005, 320 is 5.
HCF(4005, 320) = 5
HCF of 4005, 320 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 4005, 320 is 5.
Highest Common Factor of 4005,320 is 5
Step 1: Since 4005 > 320, we apply the division lemma to 4005 and 320, to get
4005 = 320 x 12 + 165
Step 2: Since the reminder 320 ≠ 0, we apply division lemma to 165 and 320, to get
320 = 165 x 1 + 155
Step 3: We consider the new divisor 165 and the new remainder 155, and apply the division lemma to get
165 = 155 x 1 + 10
We consider the new divisor 155 and the new remainder 10,and apply the division lemma to get
155 = 10 x 15 + 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 4005 and 320 is 5
Notice that 5 = HCF(10,5) = HCF(155,10) = HCF(165,155) = HCF(320,165) = HCF(4005,320) .
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Frequently Asked Questions on HCF of 4005, 320 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 4005, 320?
Answer: HCF of 4005, 320 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 4005, 320 using Euclid's Algorithm?
Answer: For arbitrary numbers 4005, 320 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.