Highest Common Factor of 960, 591 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 960, 591 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 960, 591 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 960, 591 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 960, 591 is 3.
HCF(960, 591) = 3
HCF of 960, 591 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 960, 591 is 3.
Highest Common Factor of 960,591 is 3
Step 1: Since 960 > 591, we apply the division lemma to 960 and 591, to get
960 = 591 x 1 + 369
Step 2: Since the reminder 591 ≠ 0, we apply division lemma to 369 and 591, to get
591 = 369 x 1 + 222
Step 3: We consider the new divisor 369 and the new remainder 222, and apply the division lemma to get
369 = 222 x 1 + 147
We consider the new divisor 222 and the new remainder 147,and apply the division lemma to get
222 = 147 x 1 + 75
We consider the new divisor 147 and the new remainder 75,and apply the division lemma to get
147 = 75 x 1 + 72
We consider the new divisor 75 and the new remainder 72,and apply the division lemma to get
75 = 72 x 1 + 3
We consider the new divisor 72 and the new remainder 3,and apply the division lemma to get
72 = 3 x 24 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 960 and 591 is 3
Notice that 3 = HCF(72,3) = HCF(75,72) = HCF(147,75) = HCF(222,147) = HCF(369,222) = HCF(591,369) = HCF(960,591) .
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Frequently Asked Questions on HCF of 960, 591 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 960, 591?
Answer: HCF of 960, 591 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 960, 591 using Euclid's Algorithm?
Answer: For arbitrary numbers 960, 591 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.