The Prime Factorization Of 81

Prime number Factorization Calculator

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Use this prime numbers calculator to find all prime factors of a given integer number upwards to 10 trillion. This calculator presents:

Prime factors of a number
Prime decomposition in exponential form
CSV (comma separated values) list of prime number factors
Factorization in a prime number factors tree

For the start 5000 prime numbers, this calculator indicates the index of the prime number. The northward^thursday prime is denoted as Prime[n], so Prime[one] = 2, Prime[2] = 3, Prime[3] = 5, and then on.

The limit on the input number to factor is less than 10,000,000,000,000 (less than x trillion or a maximum of 13 digits).

What is Prime Factorization?

Prime factorization or integer factorization of a number is breaking a number down into the fix of prime number numbers which multiply together to result in the original number. This is likewise known equally prime decomposition.

How to Observe Prime number Factorization of a Number

We cover two methods of prime factorization: find primes by trial division, and utilise primes to create a prime number factors tree.

Prime Factorization by Trial Division

Say yous want to observe the prime factors of 100 using trial division. Start by testing each integer to run into if and how often information technology divides 100 and the subsequent quotients evenly. The resulting gear up of factors volition be prime since, for instance, when 2 is exhausted all multiples of 2 are too wearied.

Discover the prime factors of 100:

100 ÷ 2 = 50; salve 2
l ÷ two = 25; save 2
25 ÷ 2 = 12.five, non evenly and then separate past next highest number, iii
25 ÷ 3 = 8.333, not evenly so divide by next highest number, 4
But, iv is a multiple of 2 so information technology has already been checked, and then carve up by next highest number, 5
25 ÷ five = 5; save 5
5 ÷ five = 1; salvage 5

List the resulting prime factors as a sequence of multiples, 2 10 two x 5 x v or as factors with exponents, 2² x 5².

Examples of Prime Decomposition: Factors and Exponents

Prime factorization of 100 is 2 ten 2 x 5 10 5 or 2² x v²
Prime factorization of 76 is 2 x 2 x xix or ii² ten nineteen^one
Prime factorization of 50 is 2 10 5 10 5 or 2 ten 5²
Prime factorization of 48 is 2 x 2 x two x 2 ten 3 or 2⁴ x 3¹
Prime factorization of 36 is 2 10 two x 3 x iii or 2ⁱⁱ x 3²
Prime factorization of 20 is 2 x 2 ten 5 or ii² 10 five¹
Prime factorization of x is two ten 5 or 2¹ x v¹

Prime Factors Tree

Using a prime number factorization tree to come across the work, prime decomposition of 100 = 2 x 2 ten 5 x five looks like this:

Related Calculators

For a listing of the kickoff 1000 prime numbers see our See m Prime number Numbers Table.

References and Further Reading

Math is Fun: Prime Factorization.

Weisstein, Eric West. "Prime." From MathWorld--A Wolfram Spider web Resource.

Weisstein, Eric W. "Directly Search Factorization." From MathWorld--A Wolfram Web Resource.

Weisstein, Eric Westward. "Prime number Factorization Algorithms." From MathWorld--A Wolfram Web Resources.

Caldwell, Chris Yard. The Prime Pages.

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