Highest Common Factor of 542, 992, 126 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, 992, 126 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 542, 992, 126 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 542, 992, 126 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, 992, 126 is 2.
HCF(542, 992, 126) = 2
HCF of 542, 992, 126 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, 992, 126 is 2.
Highest Common Factor of 542,992,126 is 2
Step 1: Since 992 > 542, we apply the division lemma to 992 and 542, to get
992 = 542 x 1 + 450
Step 2: Since the reminder 542 ≠ 0, we apply division lemma to 450 and 542, to get
542 = 450 x 1 + 92
Step 3: We consider the new divisor 450 and the new remainder 92, and apply the division lemma to get
450 = 92 x 4 + 82
We consider the new divisor 92 and the new remainder 82,and apply the division lemma to get
92 = 82 x 1 + 10
We consider the new divisor 82 and the new remainder 10,and apply the division lemma to get
82 = 10 x 8 + 2
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 542 and 992 is 2
Notice that 2 = HCF(10,2) = HCF(82,10) = HCF(92,82) = HCF(450,92) = HCF(542,450) = HCF(992,542) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 126 > 2, we apply the division lemma to 126 and 2, to get
126 = 2 x 63 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 126 is 2
Notice that 2 = HCF(126,2) .
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Frequently Asked Questions on HCF of 542, 992, 126 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, 992, 126?
Answer: HCF of 542, 992, 126 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 542, 992, 126 using Euclid's Algorithm?
Answer: For arbitrary numbers 542, 992, 126 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.