Highest Common Factor of 456, 585 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 456, 585 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 456, 585 is 3 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 456, 585 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 456, 585 is 3.
HCF(456, 585) = 3
HCF of 456, 585 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 456, 585 is 3.
Highest Common Factor of 456,585 is 3
Step 1: Since 585 > 456, we apply the division lemma to 585 and 456, to get
585 = 456 x 1 + 129
Step 2: Since the reminder 456 ≠ 0, we apply division lemma to 129 and 456, to get
456 = 129 x 3 + 69
Step 3: We consider the new divisor 129 and the new remainder 69, and apply the division lemma to get
129 = 69 x 1 + 60
We consider the new divisor 69 and the new remainder 60,and apply the division lemma to get
69 = 60 x 1 + 9
We consider the new divisor 60 and the new remainder 9,and apply the division lemma to get
60 = 9 x 6 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 456 and 585 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(60,9) = HCF(69,60) = HCF(129,69) = HCF(456,129) = HCF(585,456) .
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Frequently Asked Questions on HCF of 456, 585 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 456, 585?
Answer: HCF of 456, 585 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 456, 585 using Euclid's Algorithm?
Answer: For arbitrary numbers 456, 585 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
