Highest Common Factor of 640, 455 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, 455 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 640, 455 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, 455 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, 455 is 5.
HCF(640, 455) = 5
HCF of 640, 455 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, 455 is 5.
Highest Common Factor of 640,455 is 5
Step 1: Since 640 > 455, we apply the division lemma to 640 and 455, to get
640 = 455 x 1 + 185
Step 2: Since the reminder 455 ≠ 0, we apply division lemma to 185 and 455, to get
455 = 185 x 2 + 85
Step 3: We consider the new divisor 185 and the new remainder 85, and apply the division lemma to get
185 = 85 x 2 + 15
We consider the new divisor 85 and the new remainder 15,and apply the division lemma to get
85 = 15 x 5 + 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 640 and 455 is 5
Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(85,15) = HCF(185,85) = HCF(455,185) = HCF(640,455) .
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Frequently Asked Questions on HCF of 640, 455 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, 455?
Answer: HCF of 640, 455 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 640, 455 using Euclid's Algorithm?
Answer: For arbitrary numbers 640, 455 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
