Highest Common Factor of 138, 316 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, 316 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 138, 316 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 138, 316 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, 316 is 2.
HCF(138, 316) = 2
HCF of 138, 316 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, 316 is 2.
Highest Common Factor of 138,316 is 2
Step 1: Since 316 > 138, we apply the division lemma to 316 and 138, to get
316 = 138 x 2 + 40
Step 2: Since the reminder 138 ≠ 0, we apply division lemma to 40 and 138, to get
138 = 40 x 3 + 18
Step 3: We consider the new divisor 40 and the new remainder 18, and apply the division lemma to get
40 = 18 x 2 + 4
We consider the new divisor 18 and the new remainder 4,and apply the division lemma to get
18 = 4 x 4 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 138 and 316 is 2
Notice that 2 = HCF(4,2) = HCF(18,4) = HCF(40,18) = HCF(138,40) = HCF(316,138) .
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Frequently Asked Questions on HCF of 138, 316 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, 316?
Answer: HCF of 138, 316 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 138, 316 using Euclid's Algorithm?
Answer: For arbitrary numbers 138, 316 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.