Highest Common Factor of 651, 138 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 651, 138 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 651, 138 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 651, 138 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 651, 138 is 3.
HCF(651, 138) = 3
HCF of 651, 138 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 651, 138 is 3.
Highest Common Factor of 651,138 is 3
Step 1: Since 651 > 138, we apply the division lemma to 651 and 138, to get
651 = 138 x 4 + 99
Step 2: Since the reminder 138 ≠ 0, we apply division lemma to 99 and 138, to get
138 = 99 x 1 + 39
Step 3: We consider the new divisor 99 and the new remainder 39, and apply the division lemma to get
99 = 39 x 2 + 21
We consider the new divisor 39 and the new remainder 21,and apply the division lemma to get
39 = 21 x 1 + 18
We consider the new divisor 21 and the new remainder 18,and apply the division lemma to get
21 = 18 x 1 + 3
We consider the new divisor 18 and the new remainder 3,and apply the division lemma to get
18 = 3 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 651 and 138 is 3
Notice that 3 = HCF(18,3) = HCF(21,18) = HCF(39,21) = HCF(99,39) = HCF(138,99) = HCF(651,138) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 651, 138 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 651, 138?
Answer: HCF of 651, 138 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 651, 138 using Euclid's Algorithm?
Answer: For arbitrary numbers 651, 138 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.