# hello i need help please help me what is the prime factorization in exponent form for the numbers: 27 and 780 thank you

samhouston | Middle School Teacher | (Level 1) Associate Educator

Posted on

27 and 780

The easiest way to find the prime factorization of a number is using a factor tree.

27                                               780

/     \                                           /       \

3         9                                      78        10

/     \                                  /   \        /   \

3        3                              6     13    2     5

/    \

2     3

27 = 3 * 3 * 3 = 3^3

780 = 2 * 2 * 3 * 5 * 13 = 2^2 * 3 * 5 * 13

rugbykats | High School Teacher | (Level 2) Adjunct Educator

Posted on

The prime factorization of 27 is 3 x 3 x 3, which is 3^3 in exponent form.

The prime factorization of 780 is 2 x 2 x 3 x 5 x 13, which is 2^2 x 3 x 5 x 13. (Some teachers may ask you to write out the first-power exponents, which would be 2^2 x 3^1 x 5^1 x 13^1. Check your teacher's instructions, examples, etc.)

Hope this helps. Good luck!

rbrogdon | Elementary School Teacher | (Level 1) Honors

Posted on

Prime factorization means to find the prime numbers that multiply together to equal the original number. The simplest way to do this is through a factor tree. Write the original number at the top. Write two factors that multiply to equal that number. Continue until only prime numbers are left.

27                                                 780

/ \                                                  /\

9   3                                             78   10

/\                                                   /\      /\

3 3                                               2  39   2  5

/\

3 13

So, the prime factorization of 27 = 3x3x3 or 3^3.

The prime factorization of 780 = 2x2x3x5x13 or 2^2 x 3 x 5 x 13.