Highest Common Factor of 538, 932, 523 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 538, 932, 523 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 538, 932, 523 is 1 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 538, 932, 523 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 538, 932, 523 is 1.
HCF(538, 932, 523) = 1
HCF of 538, 932, 523 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 538, 932, 523 is 1.
Highest Common Factor of 538,932,523 is 1
Step 1: Since 932 > 538, we apply the division lemma to 932 and 538, to get
932 = 538 x 1 + 394
Step 2: Since the reminder 538 ≠ 0, we apply division lemma to 394 and 538, to get
538 = 394 x 1 + 144
Step 3: We consider the new divisor 394 and the new remainder 144, and apply the division lemma to get
394 = 144 x 2 + 106
We consider the new divisor 144 and the new remainder 106,and apply the division lemma to get
144 = 106 x 1 + 38
We consider the new divisor 106 and the new remainder 38,and apply the division lemma to get
106 = 38 x 2 + 30
We consider the new divisor 38 and the new remainder 30,and apply the division lemma to get
38 = 30 x 1 + 8
We consider the new divisor 30 and the new remainder 8,and apply the division lemma to get
30 = 8 x 3 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 538 and 932 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(30,8) = HCF(38,30) = HCF(106,38) = HCF(144,106) = HCF(394,144) = HCF(538,394) = HCF(932,538) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 523 > 2, we apply the division lemma to 523 and 2, to get
523 = 2 x 261 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 523 is 1
Notice that 1 = HCF(2,1) = HCF(523,2) .
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Frequently Asked Questions on HCF of 538, 932, 523 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 538, 932, 523?
Answer: HCF of 538, 932, 523 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 538, 932, 523 using Euclid's Algorithm?
Answer: For arbitrary numbers 538, 932, 523 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.