Highest Common Factor of 582, 7755 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 582, 7755 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 582, 7755 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 582, 7755 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 582, 7755 is 3.
HCF(582, 7755) = 3
HCF of 582, 7755 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 582, 7755 is 3.
Highest Common Factor of 582,7755 is 3
Step 1: Since 7755 > 582, we apply the division lemma to 7755 and 582, to get
7755 = 582 x 13 + 189
Step 2: Since the reminder 582 ≠ 0, we apply division lemma to 189 and 582, to get
582 = 189 x 3 + 15
Step 3: We consider the new divisor 189 and the new remainder 15, and apply the division lemma to get
189 = 15 x 12 + 9
We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get
15 = 9 x 1 + 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 582 and 7755 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(189,15) = HCF(582,189) = HCF(7755,582) .
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Frequently Asked Questions on HCF of 582, 7755 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 582, 7755?
Answer: HCF of 582, 7755 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 582, 7755 using Euclid's Algorithm?
Answer: For arbitrary numbers 582, 7755 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.