Highest Common Factor of 591, 720 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 591, 720 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 591, 720 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 591, 720 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 591, 720 is 3.
HCF(591, 720) = 3
HCF of 591, 720 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 591, 720 is 3.
Highest Common Factor of 591,720 is 3
Step 1: Since 720 > 591, we apply the division lemma to 720 and 591, to get
720 = 591 x 1 + 129
Step 2: Since the reminder 591 ≠ 0, we apply division lemma to 129 and 591, to get
591 = 129 x 4 + 75
Step 3: We consider the new divisor 129 and the new remainder 75, and apply the division lemma to get
129 = 75 x 1 + 54
We consider the new divisor 75 and the new remainder 54,and apply the division lemma to get
75 = 54 x 1 + 21
We consider the new divisor 54 and the new remainder 21,and apply the division lemma to get
54 = 21 x 2 + 12
We consider the new divisor 21 and the new remainder 12,and apply the division lemma to get
21 = 12 x 1 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 591 and 720 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(21,12) = HCF(54,21) = HCF(75,54) = HCF(129,75) = HCF(591,129) = HCF(720,591) .
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Frequently Asked Questions on HCF of 591, 720 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 591, 720?
Answer: HCF of 591, 720 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 591, 720 using Euclid's Algorithm?
Answer: For arbitrary numbers 591, 720 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.