Highest Common Factor of 660, 590, 872 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 660, 590, 872 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 660, 590, 872 is 2 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 660, 590, 872 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 660, 590, 872 is 2.
HCF(660, 590, 872) = 2
HCF of 660, 590, 872 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 660, 590, 872 is 2.
Highest Common Factor of 660,590,872 is 2
Step 1: Since 660 > 590, we apply the division lemma to 660 and 590, to get
660 = 590 x 1 + 70
Step 2: Since the reminder 590 ≠ 0, we apply division lemma to 70 and 590, to get
590 = 70 x 8 + 30
Step 3: We consider the new divisor 70 and the new remainder 30, and apply the division lemma to get
70 = 30 x 2 + 10
We consider the new divisor 30 and the new remainder 10, and apply the division lemma to get
30 = 10 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 660 and 590 is 10
Notice that 10 = HCF(30,10) = HCF(70,30) = HCF(590,70) = HCF(660,590) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 872 > 10, we apply the division lemma to 872 and 10, to get
872 = 10 x 87 + 2
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 2 and 10, to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 10 and 872 is 2
Notice that 2 = HCF(10,2) = HCF(872,10) .
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Frequently Asked Questions on HCF of 660, 590, 872 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 660, 590, 872?
Answer: HCF of 660, 590, 872 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 660, 590, 872 using Euclid's Algorithm?
Answer: For arbitrary numbers 660, 590, 872 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.