To find the prime factorization of 525, we will divide it by the smallest prime numbers until we can’t divide any longer.
First, we notice that 525 is an odd number, so it’s not divisible by 2. The next prime number is 3. If we sum the digits of 525 (5 + 2 + 5 = 12), we see that 12 is divisible by 3. Thus, 525 is divisible by 3:
525 ÷ 3 = 175
Next, we factor 175. It’s also an odd number, so we check for divisibility by the next prime, which is 5. Since 175 ends with a 5, it’s divisible by 5:
175 ÷ 5 = 35
Now we factor 35. Again, since it ends in 5, it is divisible by 5:
35 ÷ 5 = 7
We are left with 7, which is itself a prime number. Therefore, we can now summarize our factorizations:
525 = 3 × 5 × 5 × 7
In expanded form, we can express the prime factorization of 525 as:
525 = 3 × 52 × 7
This means that 525 can be broken down into the prime numbers 3, 5, and 7, where 5 is used twice. This gives us a complete prime factorization in expanded form.