Write 825 as a product of its Prime Factors
To find the prime factors of 825, we can start by dividing it by the smallest prime number, which is 2.
825 ÷ 2 = 412.5
Since 412.5 is not a whole number, we move on to the next prime number, which is 3.
412.5 ÷ 3 = 137.5
Again, 137.5 is not a whole number, so we continue with the next prime number, which is 5.
137.5 ÷ 5 = 27.5
Still not a whole number, we try dividing by 7.
27.5 ÷ 7 = 3.92857...
Since none of the remaining prime numbers (11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97) divide evenly into 3.92857, we can conclude that the prime factorization of 825 is:
2 × 3 × 5 × 5 × 11 = 2 × 3 × 5^2 × 11
Leave the 2 out. It is not even!
Apologies for the error. Let's find the prime factors of 825 without including 2.
825 ÷ 3 = 275
275 ÷ 5 = 55
55 ÷ 5 = 11
Since 11 is a prime number, we can conclude that the prime factorization of 825 is:
3 × 5 × 5 × 11 = 3 × 5^2 × 11
Yes,
75 * 11 is 3 * 5^2 * 11