You were assigned a locker for your books at school. You forgot the locker number but remember that two of the 12 positive factors of the locker number are 6 and 25. What is you locker number?
I calculate the answer to be 325.
Is that correct? If not will you please explain? Thank you.
hmmm. six is not a factor of 325.
6 is not a factor of 325
6 = 2*3
25 = 5*5 two factors
2*3*5*5 = 150
that is 4 factors for total of 6
then
10
30
15
75 another 4, now 10
now include 1 and 150 for 12
so I think
150
To find the locker number, you need to determine a number that has both 6 and 25 as factors. Since these are both factors, it means that the locker number must be a multiple of both 6 and 25.
Let's break down 6 and 25 into prime factors:
6 = 2 x 3
25 = 5 x 5
To find the locker number, we need to find the least common multiple (LCM) of 6 and 25. The LCM is the smallest number that is divisible by both 6 and 25.
To find the LCM, we take the highest power of each prime factor that appears in either 6 or 25:
The prime factors of 6 are 2 and 3, and the prime factors of 25 are 5 and 5.
The highest power of 2 is 2^1, the highest power of 3 is 3^1, and the highest power of 5 is 5^2.
Multiplying these together, we get the LCM:
2^1 * 3^1 * 5^2 = 2 * 3 * 25 = 150
Therefore, the locker number is 150.
So, to answer your question, the correct locker number is 150, not 325.