find the prime factorization of the following sum 12576
Answers
hi mate,
solution:
Prime Factors of 12576 =2, 2, 2, 2, 2, 3,131
Which is the same as = 2^5 x 3 x 131
Prime Factors Tree of 12576
12576
/ \
2 6288
/ \
2 3144
/ \
2 1572
/ \
2 786
/ \
2 393
/ \
3 131
The prime factors are: 2 x 2 x 2 x 2 x 2 x 3 x 131
or also written as { 2, 2, 2, 2, 2, 3, 131 }
Written in exponential form: 25 x 31 x 1311
Let's start by dividing 12,576 by 2
12,576 ÷ 2 = 6,288 - No remainder! 2 is one of the factors!
6,288 ÷ 2 = 3,144 - No remainder! 2 is one of the factors!
3,144 ÷ 2 = 1,572 - No remainder! 2 is one of the factors!
1,572 ÷ 2 = 786 - No remainder! 2 is one of the factors!
786 ÷ 2 = 393 - No remainder! 2 is one of the factors!
393 ÷ 2 = 196.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
393 ÷ 3 = 131 - No remainder! 3 is one of the factors!
131 ÷ 3 = 43.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
131 ÷ 5 = 26.2 - This has a remainder. 5 is not a factor.
131 ÷ 7 = 18.7143 - This has a remainder. 7 is not a factor.
131 ÷ 11 = 11.9091 - This has a remainder. 11 is not a factor.
Keep trying increasingly larger numbers until you find one that divides evenly.
...
131 ÷ 131 = 1 - No remainder! 131 is one of the factors!
The orange divisor(s) above are the prime factors of the number 12,576. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 2 x 3 x 131 = 12,576. It can also be written in exponential form as 25 x 31 x 1311.
i hope it helps you.