Highest Common Factor of 588, 996, 538 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, 996, 538 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 588, 996, 538 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 588, 996, 538 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, 996, 538 is 2.
HCF(588, 996, 538) = 2
HCF of 588, 996, 538 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, 996, 538 is 2.
Highest Common Factor of 588,996,538 is 2
Step 1: Since 996 > 588, we apply the division lemma to 996 and 588, to get
996 = 588 x 1 + 408
Step 2: Since the reminder 588 ≠ 0, we apply division lemma to 408 and 588, to get
588 = 408 x 1 + 180
Step 3: We consider the new divisor 408 and the new remainder 180, and apply the division lemma to get
408 = 180 x 2 + 48
We consider the new divisor 180 and the new remainder 48,and apply the division lemma to get
180 = 48 x 3 + 36
We consider the new divisor 48 and the new remainder 36,and apply the division lemma to get
48 = 36 x 1 + 12
We consider the new divisor 36 and the new remainder 12,and apply the division lemma to get
36 = 12 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 588 and 996 is 12
Notice that 12 = HCF(36,12) = HCF(48,36) = HCF(180,48) = HCF(408,180) = HCF(588,408) = HCF(996,588) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 538 > 12, we apply the division lemma to 538 and 12, to get
538 = 12 x 44 + 10
Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 10 and 12, to get
12 = 10 x 1 + 2
Step 3: We consider the new divisor 10 and the new remainder 2, and apply the division lemma 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 12 and 538 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(538,12) .
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Frequently Asked Questions on HCF of 588, 996, 538 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, 996, 538?
Answer: HCF of 588, 996, 538 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 588, 996, 538 using Euclid's Algorithm?
Answer: For arbitrary numbers 588, 996, 538 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.