The Mystery of Prime Factorization: Solving for 42

Prime factorization refers to the process of finding the prime numbers that can be multiplied to give the original number. The prime numbers are those numbers that cannot be divided evenly by any other number except for 1 and itself. Prime factorization is an essential concept for solving many mathematical problems, especially those relating to fractions, ratios, and simplifying expressions.

Now that we know what prime factorization is let’s move on to the prime factorization of 42. To figure out the prime factors of 42, we need to divide it by every prime number starting from 2. If a prime number can divide 42 evenly, we divide 42 by that number and write down the quotient. We then carry on dividing the quotient by the same prime factor until the quotient cannot be evenly divided anymore.

Let’s follow this procedure to find the prime factorization of 42:

Step 1: Divide 42 by 2

42 ÷ 2 = 21

Step 2: Divide the quotient, 21, by 2 again

21 ÷ 2 = Not possible

Step 3: Divide the original number, 42, by 3

42 ÷ 3 = 14

Step 4: Divide the quotient, 14, by 3 again

14 ÷ 3 = Not possible

Step 5: Divide the original number, 42, by 7

42 ÷ 7 = 6

Step 6: Divide the quotient, 6, by 7 again

6 ÷ 7 = Not possible

The above process shows that prime factors of 42 are 2, 3, and 7, which when multiplied together gives the original number, 42. Therefore, the prime factorization of 42 is:

2 × 3 × 7 = 42

It’s worth noting that the order in which we write the prime factors does not matter since multiplication is a commutative operation. Therefore, the prime factorization of 42 can also be written as 3 × 2 × 7 or 7 × 2 × 3.

In conclusion, prime factorization is a crucial concept that helps to simplify mathematical expressions and solve many problems. The prime factorization of 42, as we have seen, involves finding the prime numbers that can be multiplied together to give 42. The prime factors of 42 are 2, 3, and 7, and when multiplied, they give the original number, 42. This knowledge is essential for future math studies, and individuals should master it for better problem-solving skills.