Calculator Use

Use this element numbers calculator to discover all prime determinants of a provided integer number as much as 10 trillion. This calculator presents:

Prime factors of a number prime decomposition in exponential type CSV (comma be separate values) perform of prime components Factorization in a prime components tree

For the an initial 5000 element numbers, this calculator suggests the table of contents of the element number. The nth element number is denoted as Prime, so Prime<1> = 2, Prime<2> = 3, Prime<3> = 5, and also so on.

The limit on the entry number to element is much less than 10,000,000,000,000 (less than 10 sunshine or a maximum of 13 digits).

You are watching: Prime factorization of 15 using exponents

What is prime Factorization?

Prime administer or integer factorization that a number is break a number down into the set of element numbers i beg your pardon multiply with each other to result in the original number. This is also known together prime decomposition.

How to uncover Prime factorization of a Number

We cover two approaches of prime factorization: uncover primes by trial division, and also use primes to produce a prime factors tree.

See more: Oxidation Number Of S In Magnesium Sulfate, Oxidation States (Oxidation Numbers)

Prime administer by attempt Division

Say you desire to find the prime components of 100 making use of trial division. Begin by experimentation each essence to watch if and how frequently it divides 100 and also the subsequent quotients evenly. The resulting set of determinants will be prime since, for example, as soon as 2 is exhausted all multiples that 2 are also exhausted.

Find the prime components of 100:

100 ÷ 2 = 50; save 2 50 ÷ 2 = 25; conserve 2 25 ÷ 2 = 12.5, not evenly so divide by next highest possible number, 3 25 ÷ 3 = 8.333, no evenly so divide by next highest possible number, 4 But, 4 is a lot of of 2 so the has currently been checked, so division by next greatest number, 5 25 ÷ 5 = 5; save 5 5 ÷ 5 = 1; save 5

List the result prime factors as a succession of multiples, 2 x 2 x 5 x 5 or as factors with exponents, 22 x 52.

Examples of prime Decomposition: Factors and also Exponents

prime factorization that 100 is 2 x 2 x 5 x 5 or 22 x 52 prime factorization of 76 is 2 x 2 x 19 or 22 x 191 prime factorization the 50 is 2 x 5 x 5 or 2 x 52 prime factorization the 48 is 2 x 2 x 2 x 2 x 3 or 24 x 31 element factorization that 36 is 2 x 2 x 3 x 3 or 22 x 32 element factorization the 20 is 2 x 2 x 5 or 22 x 51 element factorization of 10 is 2 x 5 or 21 x 51

Prime factors Tree

Using a prime factorization tree to watch the work, prime decomposition the 100 = 2 x 2 x 5 x 5 looks choose this: