Highest Common Factor of 360, 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 360, 585 i.e. 45 the largest integer that leaves a remainder zero for all numbers.
HCF of 360, 585 is 45 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 360, 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 360, 585 is 45.
HCF(360, 585) = 45
HCF of 360, 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 360, 585 is 45.
Highest Common Factor of 360,585 is 45
Step 1: Since 585 > 360, we apply the division lemma to 585 and 360, to get
585 = 360 x 1 + 225
Step 2: Since the reminder 360 ≠ 0, we apply division lemma to 225 and 360, to get
360 = 225 x 1 + 135
Step 3: We consider the new divisor 225 and the new remainder 135, and apply the division lemma to get
225 = 135 x 1 + 90
We consider the new divisor 135 and the new remainder 90,and apply the division lemma to get
135 = 90 x 1 + 45
We consider the new divisor 90 and the new remainder 45,and apply the division lemma to get
90 = 45 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 45, the HCF of 360 and 585 is 45
Notice that 45 = HCF(90,45) = HCF(135,90) = HCF(225,135) = HCF(360,225) = HCF(585,360) .
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Frequently Asked Questions on HCF of 360, 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 360, 585?
Answer: HCF of 360, 585 is 45 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 360, 585 using Euclid's Algorithm?
Answer: For arbitrary numbers 360, 585 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
