Question

Write the prime factorization of 1008 and 1323. Then
reduce 1008/1323

Answer 1

The prime factorization of 1008 is:

1008 = 2^4 × 3^2 × 7

The prime factorization of 1323 is:

1323 = 3 × 19 × 23

To reduce 1008/1323, we need to simplify the fraction by dividing the numerator and denominator by their greatest common factor (GCF). To find the GCF of 1008 and 1323, we can use their prime factorizations. The only common prime factor they share is 3, so the GCF is 3.

1008/1323 = (3 × 336)/(3 × 441) = 336/441

We can simplify this fraction further by dividing both the numerator and denominator by 7, which is the GCF of 336 and 441.

336/441 = (7 × 48)/(7 × 63) = 48/63

Finally, we can simplify this fraction by dividing both the numerator and denominator by their GCF, which is 3.

48/63 = (3 × 16)/(3 × 21) = 16/21

Therefore, 1008/1323 simplified is 16/21.

Step-by-step explanation:

Answer 2

The prime factorization of 1008 is 2^4 * 3^2 * 7 and the prime factorization of 1323 is 3 * 13^2. The reduced fraction of 1008/1323 is 336/441.

Step-by-step explanation:

The prime factorization of 1008 is 2^4 * 3^2 * 7 and the prime factorization of 1323 is 3 * 13^2. To find the prime factorization of a number, you divide the number by the smallest prime factors starting from 2. Divide the number by 2 until it is no longer divisible, then move on to the next smallest prime number. Then, to reduce 1008/1323, you can cancel out any common factors in the numerator and denominator. In this case, only the factor 3 is common, so you can divide both numbers by 3. The reduced fraction is 336/441.