Highest Common Factor of 285, 505, 656 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 285, 505, 656 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 285, 505, 656 is 1 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 285, 505, 656 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 285, 505, 656 is 1.
HCF(285, 505, 656) = 1
HCF of 285, 505, 656 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 285, 505, 656 is 1.
Highest Common Factor of 285,505,656 is 1
Step 1: Since 505 > 285, we apply the division lemma to 505 and 285, to get
505 = 285 x 1 + 220
Step 2: Since the reminder 285 ≠ 0, we apply division lemma to 220 and 285, to get
285 = 220 x 1 + 65
Step 3: We consider the new divisor 220 and the new remainder 65, and apply the division lemma to get
220 = 65 x 3 + 25
We consider the new divisor 65 and the new remainder 25,and apply the division lemma to get
65 = 25 x 2 + 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 285 and 505 is 5
Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(25,15) = HCF(65,25) = HCF(220,65) = HCF(285,220) = HCF(505,285) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 656 > 5, we apply the division lemma to 656 and 5, to get
656 = 5 x 131 + 1
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 1 and 5, to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 656 is 1
Notice that 1 = HCF(5,1) = HCF(656,5) .
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Frequently Asked Questions on HCF of 285, 505, 656 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 285, 505, 656?
Answer: HCF of 285, 505, 656 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 285, 505, 656 using Euclid's Algorithm?
Answer: For arbitrary numbers 285, 505, 656 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.