Write each number as the product of prime factors.
11. 110
13.180
15.441
17. 1080
11. 110 = 2 * 5 * 11
13. 180 = 2 * 2 * 3 * 3 * 5
15. 441 = 3 * 3 * 7 * 7
17. 1080 = 2 * 2 * 2 * 3 * 3 * 3 * 5
To write each number as the product of prime factors, we need to find the prime factors of each number.
1. For 110:
To find the prime factors of 110, we can start by dividing it by the smallest prime number, 2. Since 110 is even, we can divide it by 2, and we get 55. 55 is not divisible by 2, so we move on to the next prime number, which is 3. 55 divided by 3 is not a whole number, so we move on to 5. 55 divided by 5 is equal to 11, which is a prime number. Therefore, the prime factors of 110 are 2, 5, and 11.
2. For 180:
To find the prime factors of 180, we start by dividing it by 2. 180 divided by 2 is equal to 90, which is divisible by 2. So, we divide 90 by 2 again, resulting in 45. 45 is divisible by 3, so we divide it by 3, giving us 15. Finally, 15 is divisible by 5, so dividing it by 5 yields 3. Therefore, the prime factors of 180 are 2, 2, 3, 3, and 5.
3. For 441:
To find the prime factors of 441, we can start by dividing it by 3. 441 divided by 3 is 147, which is also divisible by 3. Dividing 147 by 3 gives us 49, which is a perfect square of 7. Therefore, the prime factors of 441 are 3, 3, and 7.
4. For 1080:
To find the prime factors of 1080, we can start by dividing it by 2. 1080 divided by 2 is equal to 540, which is also divisible by 2. So, we divide 540 by 2 again, resulting in 270. 270 is divisible by 2, so dividing it by 2 gives us 135. 135 is divisible by 3, so we divide it by 3, resulting in 45. Finally, 45 is divisible by 5, so dividing it by 5 gives us 9, which is a perfect square of 3. Therefore, the prime factors of 1080 are 2, 2, 2, 3, 3, 3, and 5.