You can use the prime factorization of a number, written
as the product of powers of prime numbers, to find
the number of factors the number has. First, express the
number as a product of powers of prime numbers; for
example, 36=2 to power 2 3 to power 3
Then increase each exponent by 1,
and find the product of these increased exponents. This
product is the number of factors of the number. In the
example for 36,(2+1)(2+1) so 36 has 9 factors.
how do i write 48 as a product of powers of prime numbers
Jessica, Chandice, and Thomas or whoever -- please post your attempts to answer these 8 questions.
To write 48 as a product of powers of prime numbers, we need to find its prime factors.
Step 1: Start by dividing 48 by the smallest prime number, which is 2. We get 48 ÷ 2 = 24.
Step 2: Since 24 is also divisible by 2, we divide it again: 24 ÷ 2 = 12.
Step 3: Now we continue dividing by 2: 12 ÷ 2 = 6.
Step 4: We divide by 2 again: 6 ÷ 2 = 3.
Step 5: At this point, we cannot divide 3 any further, so we move on to the next prime number, which is 3 itself.
Step 6: We divide 3 by 3, giving us 1.
Now we have expressed 48 as a product of powers of prime numbers: 48 = 2^4 * 3^1.