Highest Common Factor of 138, 659 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, 659 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 138, 659 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, 659 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, 659 is 1.
HCF(138, 659) = 1
HCF of 138, 659 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, 659 is 1.
Highest Common Factor of 138,659 is 1
Step 1: Since 659 > 138, we apply the division lemma to 659 and 138, to get
659 = 138 x 4 + 107
Step 2: Since the reminder 138 ≠ 0, we apply division lemma to 107 and 138, to get
138 = 107 x 1 + 31
Step 3: We consider the new divisor 107 and the new remainder 31, and apply the division lemma to get
107 = 31 x 3 + 14
We consider the new divisor 31 and the new remainder 14,and apply the division lemma to get
31 = 14 x 2 + 3
We consider the new divisor 14 and the new remainder 3,and apply the division lemma to get
14 = 3 x 4 + 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 138 and 659 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(31,14) = HCF(107,31) = HCF(138,107) = HCF(659,138) .
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Frequently Asked Questions on HCF of 138, 659 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, 659?
Answer: HCF of 138, 659 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 138, 659 using Euclid's Algorithm?
Answer: For arbitrary numbers 138, 659 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.