Highest Common Factor of 137, 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 137, 81 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 137, 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 137, 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 137, 81 is 1.
HCF(137, 81) = 1
HCF of 137, 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 137, 81 is 1.
Highest Common Factor of 137,81 is 1
Step 1: Since 137 > 81, we apply the division lemma to 137 and 81, to get
137 = 81 x 1 + 56
Step 2: Since the reminder 81 ≠ 0, we apply division lemma to 56 and 81, to get
81 = 56 x 1 + 25
Step 3: We consider the new divisor 56 and the new remainder 25, and apply the division lemma to get
56 = 25 x 2 + 6
We consider the new divisor 25 and the new remainder 6,and apply the division lemma to get
25 = 6 x 4 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 137 and 81 is 1
Notice that 1 = HCF(6,1) = HCF(25,6) = HCF(56,25) = HCF(81,56) = HCF(137,81) .
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Frequently Asked Questions on HCF of 137, 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 137, 81?
Answer: HCF of 137, 81 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 137, 81 using Euclid's Algorithm?
Answer: For arbitrary numbers 137, 81 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.