how can I make a factorization string for the number 48?
ok here we go
48
2-24 then
2-12 then
2-6
then 2-6
48
2*24 then
2*2*12 then
2*2*2*6 then
2*2*2*2*3
To make a factorization string for the number 48, you need to find all the prime factors of 48 and list them with their respective exponents. Here's how you can do it:
1. Start by finding the smallest prime factor of 48, which is 2. Divide 48 by 2 to get 24. Write down "2" as the first factor.
2. Next, continue dividing the quotient (24) by 2 until you can no longer divide evenly. You will find that 24 ÷ 2 = 12. Write down another "2" as the next factor, making it "2^2" since you divided twice by 2.
3. Repeat the process for the new quotient, which is 12. Divide it by 2 again to get 6. Write down another "2," making it "2^3" since you divided three times by 2.
4. Now, try dividing the quotient (6) by the smallest prime factor greater than 2, which is 3. Divide 6 by 3 to get 2. Write down a "3" as the next factor, making it "2^3 × 3" so far.
5. Finally, check if the quotient (2) itself is a prime number or divisible by any other prime numbers. In this case, 2 is a prime number, so we can multiply our factorization string with "2" to get the final result.
Putting it all together, the factorization string for the number 48 is "2^4 × 3."