Highest Common Factor of 142, 537, 462 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 142, 537, 462 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 142, 537, 462 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 142, 537, 462 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 142, 537, 462 is 1.
HCF(142, 537, 462) = 1
HCF of 142, 537, 462 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 142, 537, 462 is 1.
Highest Common Factor of 142,537,462 is 1
Step 1: Since 537 > 142, we apply the division lemma to 537 and 142, to get
537 = 142 x 3 + 111
Step 2: Since the reminder 142 ≠ 0, we apply division lemma to 111 and 142, to get
142 = 111 x 1 + 31
Step 3: We consider the new divisor 111 and the new remainder 31, and apply the division lemma to get
111 = 31 x 3 + 18
We consider the new divisor 31 and the new remainder 18,and apply the division lemma to get
31 = 18 x 1 + 13
We consider the new divisor 18 and the new remainder 13,and apply the division lemma to get
18 = 13 x 1 + 5
We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get
13 = 5 x 2 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 142 and 537 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(18,13) = HCF(31,18) = HCF(111,31) = HCF(142,111) = HCF(537,142) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 462 > 1, we apply the division lemma to 462 and 1, to get
462 = 1 x 462 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 462 is 1
Notice that 1 = HCF(462,1) .
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Frequently Asked Questions on HCF of 142, 537, 462 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 142, 537, 462?
Answer: HCF of 142, 537, 462 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 142, 537, 462 using Euclid's Algorithm?
Answer: For arbitrary numbers 142, 537, 462 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.