Highest Common Factor of 222, 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 222, 585 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 222, 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 222, 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 222, 585 is 3.
HCF(222, 585) = 3
HCF of 222, 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 222, 585 is 3.
Highest Common Factor of 222,585 is 3
Step 1: Since 585 > 222, we apply the division lemma to 585 and 222, to get
585 = 222 x 2 + 141
Step 2: Since the reminder 222 ≠ 0, we apply division lemma to 141 and 222, to get
222 = 141 x 1 + 81
Step 3: We consider the new divisor 141 and the new remainder 81, and apply the division lemma to get
141 = 81 x 1 + 60
We consider the new divisor 81 and the new remainder 60,and apply the division lemma to get
81 = 60 x 1 + 21
We consider the new divisor 60 and the new remainder 21,and apply the division lemma to get
60 = 21 x 2 + 18
We consider the new divisor 21 and the new remainder 18,and apply the division lemma to get
21 = 18 x 1 + 3
We consider the new divisor 18 and the new remainder 3,and apply the division lemma to get
18 = 3 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 222 and 585 is 3
Notice that 3 = HCF(18,3) = HCF(21,18) = HCF(60,21) = HCF(81,60) = HCF(141,81) = HCF(222,141) = HCF(585,222) .
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Frequently Asked Questions on HCF of 222, 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 222, 585?
Answer: HCF of 222, 585 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 222, 585 using Euclid's Algorithm?
Answer: For arbitrary numbers 222, 585 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.