Highest Common Factor of 905, 555, 285 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 905, 555, 285 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 905, 555, 285 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 905, 555, 285 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 905, 555, 285 is 5.
HCF(905, 555, 285) = 5
HCF of 905, 555, 285 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 905, 555, 285 is 5.
Highest Common Factor of 905,555,285 is 5
Step 1: Since 905 > 555, we apply the division lemma to 905 and 555, to get
905 = 555 x 1 + 350
Step 2: Since the reminder 555 ≠ 0, we apply division lemma to 350 and 555, to get
555 = 350 x 1 + 205
Step 3: We consider the new divisor 350 and the new remainder 205, and apply the division lemma to get
350 = 205 x 1 + 145
We consider the new divisor 205 and the new remainder 145,and apply the division lemma to get
205 = 145 x 1 + 60
We consider the new divisor 145 and the new remainder 60,and apply the division lemma to get
145 = 60 x 2 + 25
We consider the new divisor 60 and the new remainder 25,and apply the division lemma to get
60 = 25 x 2 + 10
We consider the new divisor 25 and the new remainder 10,and apply the division lemma to get
25 = 10 x 2 + 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 905 and 555 is 5
Notice that 5 = HCF(10,5) = HCF(25,10) = HCF(60,25) = HCF(145,60) = HCF(205,145) = HCF(350,205) = HCF(555,350) = HCF(905,555) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 285 > 5, we apply the division lemma to 285 and 5, to get
285 = 5 x 57 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5 and 285 is 5
Notice that 5 = HCF(285,5) .
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Frequently Asked Questions on HCF of 905, 555, 285 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 905, 555, 285?
Answer: HCF of 905, 555, 285 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 905, 555, 285 using Euclid's Algorithm?
Answer: For arbitrary numbers 905, 555, 285 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.