Highest Common Factor of 588, 372, 75 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 588, 372, 75 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 588, 372, 75 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 588, 372, 75 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 588, 372, 75 is 3.
HCF(588, 372, 75) = 3
HCF of 588, 372, 75 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 588, 372, 75 is 3.
Highest Common Factor of 588,372,75 is 3
Step 1: Since 588 > 372, we apply the division lemma to 588 and 372, to get
588 = 372 x 1 + 216
Step 2: Since the reminder 372 ≠ 0, we apply division lemma to 216 and 372, to get
372 = 216 x 1 + 156
Step 3: We consider the new divisor 216 and the new remainder 156, and apply the division lemma to get
216 = 156 x 1 + 60
We consider the new divisor 156 and the new remainder 60,and apply the division lemma to get
156 = 60 x 2 + 36
We consider the new divisor 60 and the new remainder 36,and apply the division lemma to get
60 = 36 x 1 + 24
We consider the new divisor 36 and the new remainder 24,and apply the division lemma to get
36 = 24 x 1 + 12
We consider the new divisor 24 and the new remainder 12,and apply the division lemma to get
24 = 12 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 588 and 372 is 12
Notice that 12 = HCF(24,12) = HCF(36,24) = HCF(60,36) = HCF(156,60) = HCF(216,156) = HCF(372,216) = HCF(588,372) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 75 > 12, we apply the division lemma to 75 and 12, to get
75 = 12 x 6 + 3
Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 3 and 12, to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 12 and 75 is 3
Notice that 3 = HCF(12,3) = HCF(75,12) .
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Frequently Asked Questions on HCF of 588, 372, 75 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 588, 372, 75?
Answer: HCF of 588, 372, 75 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 588, 372, 75 using Euclid's Algorithm?
Answer: For arbitrary numbers 588, 372, 75 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
