Highest Common Factor of 132, 376, 668, 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 132, 376, 668, 538 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 132, 376, 668, 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 132, 376, 668, 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 132, 376, 668, 538 is 2.
HCF(132, 376, 668, 538) = 2
HCF of 132, 376, 668, 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 132, 376, 668, 538 is 2.
Highest Common Factor of 132,376,668,538 is 2
Step 1: Since 376 > 132, we apply the division lemma to 376 and 132, to get
376 = 132 x 2 + 112
Step 2: Since the reminder 132 ≠ 0, we apply division lemma to 112 and 132, to get
132 = 112 x 1 + 20
Step 3: We consider the new divisor 112 and the new remainder 20, and apply the division lemma to get
112 = 20 x 5 + 12
We consider the new divisor 20 and the new remainder 12,and apply the division lemma to get
20 = 12 x 1 + 8
We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get
12 = 8 x 1 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 132 and 376 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(20,12) = HCF(112,20) = HCF(132,112) = HCF(376,132) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 668 > 4, we apply the division lemma to 668 and 4, to get
668 = 4 x 167 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 668 is 4
Notice that 4 = HCF(668,4) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 538 > 4, we apply the division lemma to 538 and 4, to get
538 = 4 x 134 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4 and 538 is 2
Notice that 2 = HCF(4,2) = HCF(538,4) .
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Frequently Asked Questions on HCF of 132, 376, 668, 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 132, 376, 668, 538?
Answer: HCF of 132, 376, 668, 538 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 132, 376, 668, 538 using Euclid's Algorithm?
Answer: For arbitrary numbers 132, 376, 668, 538 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.