Prime Factoization of 504.

Prime Factorization of 1080.

Use the factor tree method to solve both questions.

To find the prime factorization of a number, you need to determine the prime numbers that divide it exactly.

To find the prime factorization of 504, you can follow these steps:

1. Start by dividing the number by the smallest prime number, which is 2. Since 504 is an even number, we can divide it by 2 as many times as possible.
504 ÷ 2 = 252

2. Now, we repeat step 1 with the quotient obtained in the previous step, which is 252.
252 ÷ 2 = 126

3. Continuing with the next quotient, which is 126:
126 ÷ 2 = 63

4. Again, divide the quotient (63) by 2:
63 ÷ 2 = 31.5

Since 31.5 is not a whole number, we move on to the next prime number.

5. Divide the current quotient (63) by 3:
63 ÷ 3 = 21

6. Continue dividing the quotient (21) by 3:
21 ÷ 3 = 7

At this point, we have obtained the prime factorization of 504: 2 × 2 × 2 × 3 × 3 × 7 = 2^3 × 3^2 × 7.

Now let's calculate the prime factorization of 1080:

1. Divide the number by 2:
1080 ÷ 2 = 540

2. Divide the quotient (540) by 2:
540 ÷ 2 = 270

3. Divide the new quotient (270) by 2:
270 ÷ 2 = 135

4. Continuing with the current quotient (135), divide it by 3:
135 ÷ 3 = 45

5. Divide the quotient (45) by 3:
45 ÷ 3 = 15

6. Divide the quotient (15) by 5:
15 ÷ 5 = 3

At this point, we have the prime factorization of 1080: 2 × 2 × 2 × 3 × 3 × 3 × 5 = 2^3 × 3^3 × 5.