Highest Common Factor of 542, 412, 523, 41 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 542, 412, 523, 41 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 542, 412, 523, 41 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 542, 412, 523, 41 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 542, 412, 523, 41 is 1.
HCF(542, 412, 523, 41) = 1
HCF of 542, 412, 523, 41 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 542, 412, 523, 41 is 1.
Highest Common Factor of 542,412,523,41 is 1
Step 1: Since 542 > 412, we apply the division lemma to 542 and 412, to get
542 = 412 x 1 + 130
Step 2: Since the reminder 412 ≠ 0, we apply division lemma to 130 and 412, to get
412 = 130 x 3 + 22
Step 3: We consider the new divisor 130 and the new remainder 22, and apply the division lemma to get
130 = 22 x 5 + 20
We consider the new divisor 22 and the new remainder 20,and apply the division lemma to get
22 = 20 x 1 + 2
We consider the new divisor 20 and the new remainder 2,and apply the division lemma to get
20 = 2 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 542 and 412 is 2
Notice that 2 = HCF(20,2) = HCF(22,20) = HCF(130,22) = HCF(412,130) = HCF(542,412) .
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) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 41 > 1, we apply the division lemma to 41 and 1, to get
41 = 1 x 41 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 41 is 1
Notice that 1 = HCF(41,1) .
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Frequently Asked Questions on HCF of 542, 412, 523, 41 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 542, 412, 523, 41?
Answer: HCF of 542, 412, 523, 41 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 542, 412, 523, 41 using Euclid's Algorithm?
Answer: For arbitrary numbers 542, 412, 523, 41 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.