Highest Common Factor of 455, 660 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 455, 660 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 455, 660 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 455, 660 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 455, 660 is 5.
HCF(455, 660) = 5
HCF of 455, 660 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 455, 660 is 5.
Highest Common Factor of 455,660 is 5
Step 1: Since 660 > 455, we apply the division lemma to 660 and 455, to get
660 = 455 x 1 + 205
Step 2: Since the reminder 455 ≠ 0, we apply division lemma to 205 and 455, to get
455 = 205 x 2 + 45
Step 3: We consider the new divisor 205 and the new remainder 45, and apply the division lemma to get
205 = 45 x 4 + 25
We consider the new divisor 45 and the new remainder 25,and apply the division lemma to get
45 = 25 x 1 + 20
We consider the new divisor 25 and the new remainder 20,and apply the division lemma to get
25 = 20 x 1 + 5
We consider the new divisor 20 and the new remainder 5,and apply the division lemma to get
20 = 5 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 455 and 660 is 5
Notice that 5 = HCF(20,5) = HCF(25,20) = HCF(45,25) = HCF(205,45) = HCF(455,205) = HCF(660,455) .
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Frequently Asked Questions on HCF of 455, 660 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 455, 660?
Answer: HCF of 455, 660 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 455, 660 using Euclid's Algorithm?
Answer: For arbitrary numbers 455, 660 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.