Use the HCF using Euclid’s division lemma Calculator an online tool to get the highest common factor of numbers quickly and easily. Insert the number in their place and click the “calculate” button to get the solution.
HCF Using Euclid's division lemma Calculator:
Is finding the HCF of a number using Euclid’s division lemma difficult? Take help from our tool HCF Using Euclid’s Divison Lemma Calculator. It will solve your question with a brief explanation of the procedure alongside. For a better understanding have a look at the examples provided below.
The Highest Common Factor (HCF) Calculator is used to calculate GCF of two or more whole numbers. Here, you can enter numbers separated by a comma “,” and then press the Calculate button to get the HCF of those numbers using the Euclidean division algorithm.
Here are some samples of HCF Using Euclids Division Algorithm calculations.
The basis of the Euclidean division algorithm is Euclid’s division lemma. Euclid’s division algorithm is a method to calculate the Highest Common Factor (HCF) of two or three given positive numbers. Euclid’s Division Lemma says that for any two positive integers suppose a and b there exist two novel whole numbers say q and r, such that, a = bq+r, where 0≤r
Here, a and b are given numbers whereas q and r are Quotient and Reminder.
To find the Highest Common Factor (HCF) of two positive integers a and b we use Euclid’s division algorithm. Highest Common Factor (HCF) of two or more numbers is the greatest common factor of the given set of numbers. If we consider two numbers to find the HCF using Euclid’s Division Lemma Algorithm then we need to choose the largest integer first to satisfy the statement, a = bq+r where 0 ≤ r ≤ b.
Let’s get deep to see how the algorithm works when finding the HCF of two or more given numbers.
Euclid’s Division Lemma states that if we have two positive integers a and b, then there are unique integers q and r which satisfies the requirement,
a = bq + r
here, 0 ≤ r < b.
The Euclidean division algorithm is based on Euclid’s division lemma. It is also called the long division process.
Mathematically, this algorithm can be expressed as a dividend that will be equal to a divisor multiplied by the quotient added with the remainder i.e represented as Dividend = (Divisor × Quotient) + Remainder.
Euclid’s division lemma is used to compute the Highest Common Factor (HCF) of a pair of positive integers a and b. As H.C.F is the largest number which divides two or more positive integers exactly. This implies, that on dividing both the integers a and b the outcome is zero.
To evaluate the HCF of two positive integers, let's take them as c and d, with c > d, proceed with the following steps below:
c = DQ + r, 0 ≤ r < d.
Special Case: If One of the Two Original Numbers is 0
As mentioned above if,
r = 0
Then d will be the HCF of c and d.
In other words,
If (x, 0) are two numbers,
Then HCF of x and 0 will be x
i.e HCF(x, 0) = x
Because zero has infinite factors.
Use Euclid's division algorithm to find the HCF of 276 and 726.
726 > 275
This, by applying Euclid's division lemma to 726 with 275 as the divisor,
726 = 275 × 2 + 176
275 = 176 × 1 + 99
176 = 99 × 1 + 77
99 = 77 × 1 + 22
77 = 22 × 3 + 11
22 = 11 × 2 + 0
Finally, the remainder is zero. So the process stops with this step.
The divisor at this phase is 11. So, the HCF(726, 275) = 11.
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By applying the Euclid division lemma we can determine the HCF of 867 and 255 as 51.
We can use Euclid's division lemma to determine the HCF of two large numbers using the statement,
'a = bq +r' , where 0 ≤ r < b.
We can simply represent the lemma as Dividend = (Divisor × Quotient) + Remainder. For example 9=(4×2)+1
This is a simple technique required to calculate the HCF for any two numbers (positive integers).