Highest Common Factor of 640, 465 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 640, 465 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 640, 465 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 640, 465 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 640, 465 is 5.
HCF(640, 465) = 5
HCF of 640, 465 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 640, 465 is 5.
Highest Common Factor of 640,465 is 5
Step 1: Since 640 > 465, we apply the division lemma to 640 and 465, to get
640 = 465 x 1 + 175
Step 2: Since the reminder 465 ≠ 0, we apply division lemma to 175 and 465, to get
465 = 175 x 2 + 115
Step 3: We consider the new divisor 175 and the new remainder 115, and apply the division lemma to get
175 = 115 x 1 + 60
We consider the new divisor 115 and the new remainder 60,and apply the division lemma to get
115 = 60 x 1 + 55
We consider the new divisor 60 and the new remainder 55,and apply the division lemma to get
60 = 55 x 1 + 5
We consider the new divisor 55 and the new remainder 5,and apply the division lemma to get
55 = 5 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 640 and 465 is 5
Notice that 5 = HCF(55,5) = HCF(60,55) = HCF(115,60) = HCF(175,115) = HCF(465,175) = HCF(640,465) .
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Frequently Asked Questions on HCF of 640, 465 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 640, 465?
Answer: HCF of 640, 465 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 640, 465 using Euclid's Algorithm?
Answer: For arbitrary numbers 640, 465 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.