Highest Common Factor of 388, 142, 81 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 388, 142, 81 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 388, 142, 81 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 388, 142, 81 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 388, 142, 81 is 1.
HCF(388, 142, 81) = 1
HCF of 388, 142, 81 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 388, 142, 81 is 1.
Highest Common Factor of 388,142,81 is 1
Step 1: Since 388 > 142, we apply the division lemma to 388 and 142, to get
388 = 142 x 2 + 104
Step 2: Since the reminder 142 ≠ 0, we apply division lemma to 104 and 142, to get
142 = 104 x 1 + 38
Step 3: We consider the new divisor 104 and the new remainder 38, and apply the division lemma to get
104 = 38 x 2 + 28
We consider the new divisor 38 and the new remainder 28,and apply the division lemma to get
38 = 28 x 1 + 10
We consider the new divisor 28 and the new remainder 10,and apply the division lemma to get
28 = 10 x 2 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 388 and 142 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(28,10) = HCF(38,28) = HCF(104,38) = HCF(142,104) = HCF(388,142) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 81 > 2, we apply the division lemma to 81 and 2, to get
81 = 2 x 40 + 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 81 is 1
Notice that 1 = HCF(2,1) = HCF(81,2) .
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Frequently Asked Questions on HCF of 388, 142, 81 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 388, 142, 81?
Answer: HCF of 388, 142, 81 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 388, 142, 81 using Euclid's Algorithm?
Answer: For arbitrary numbers 388, 142, 81 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.