Highest Common Factor of 138, 639 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, 639 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 138, 639 is 3 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, 639 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, 639 is 3.
HCF(138, 639) = 3
HCF of 138, 639 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, 639 is 3.
Highest Common Factor of 138,639 is 3
Step 1: Since 639 > 138, we apply the division lemma to 639 and 138, to get
639 = 138 x 4 + 87
Step 2: Since the reminder 138 ≠ 0, we apply division lemma to 87 and 138, to get
138 = 87 x 1 + 51
Step 3: We consider the new divisor 87 and the new remainder 51, and apply the division lemma to get
87 = 51 x 1 + 36
We consider the new divisor 51 and the new remainder 36,and apply the division lemma to get
51 = 36 x 1 + 15
We consider the new divisor 36 and the new remainder 15,and apply the division lemma to get
36 = 15 x 2 + 6
We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get
15 = 6 x 2 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 138 and 639 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(36,15) = HCF(51,36) = HCF(87,51) = HCF(138,87) = HCF(639,138) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 138, 639 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, 639?
Answer: HCF of 138, 639 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 138, 639 using Euclid's Algorithm?
Answer: For arbitrary numbers 138, 639 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.