Highest Common Factor of 138, 377, 842 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 138, 377, 842 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 138, 377, 842 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 138, 377, 842 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 138, 377, 842 is 1.
HCF(138, 377, 842) = 1
HCF of 138, 377, 842 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 138, 377, 842 is 1.
Highest Common Factor of 138,377,842 is 1
Step 1: Since 377 > 138, we apply the division lemma to 377 and 138, to get
377 = 138 x 2 + 101
Step 2: Since the reminder 138 ≠ 0, we apply division lemma to 101 and 138, to get
138 = 101 x 1 + 37
Step 3: We consider the new divisor 101 and the new remainder 37, and apply the division lemma to get
101 = 37 x 2 + 27
We consider the new divisor 37 and the new remainder 27,and apply the division lemma to get
37 = 27 x 1 + 10
We consider the new divisor 27 and the new remainder 10,and apply the division lemma to get
27 = 10 x 2 + 7
We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get
10 = 7 x 1 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 138 and 377 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(27,10) = HCF(37,27) = HCF(101,37) = HCF(138,101) = HCF(377,138) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 842 > 1, we apply the division lemma to 842 and 1, to get
842 = 1 x 842 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 842 is 1
Notice that 1 = HCF(842,1) .
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Frequently Asked Questions on HCF of 138, 377, 842 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 138, 377, 842?
Answer: HCF of 138, 377, 842 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 138, 377, 842 using Euclid's Algorithm?
Answer: For arbitrary numbers 138, 377, 842 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.