To find the prime factorization of 48, we start by dividing the number by the smallest prime number, which is 2.
1. First, we calculate:
48 ÷ 2 = 24
2. Next, we divide 24 by 2 again:
24 ÷ 2 = 12
3. Continuing, we divide 12 by 2:
12 ÷ 2 = 6
4. And again, we divide 6 by 2:
6 ÷ 2 = 3
5. Now, we’ve reached the number 3, which is a prime number and cannot be divided by 2 anymore. We can also divide:
3 ÷ 3 = 1
So, the complete prime factorization of 48 is:
2 × 2 × 2 × 2 × 3
In exponential form, we can express it as:
24 × 3
Therefore, the prime factorization of 48 is 24 × 3.
Understanding prime factorization is essential for various applications in mathematics, including simplifying fractions and finding the least common multiple and greatest common divisor. Knowing how to break a number down can be incredibly useful in both academic and practical scenarios!