Understanding Prime Factorization
Prime factorization is the process of expressing a number as the product of its prime factors. For the number 3572, we will break it down step by step.
Step 1: Check for Divisibility by 2
- 3572 is an even number, so it is divisible by 2.
- Dividing 3572 by 2 gives us 1786.
Step 2: Continue Dividing by 2
- 1786 is also even, so we divide it again by 2.
- 1786 ÷ 2 = 893.
Step 3: Check for Other Prime Factors
- Now, we need to check if 893 is a prime number.
- It is not divisible by 2 (since it's odd), so we check for divisibility by 3, 5, 7, 11, and 13.
Step 4: Finding Prime Factors of 893
- 893 is divisible by 19 (893 ÷ 19 = 47).
- Both 19 and 47 are prime numbers.
Final Prime Factorization
- The complete prime factorization of 3572 can now be written as:
- 2 × 2 × 19 × 47
- This can also be expressed as 2² × 19 × 47.
Summary of Prime Factorization
- The prime factors of 3572 are:
- 2 (twice)
- 19
- 47
Thus, the prime factorization of 3572 is 2² × 19 × 47. This methodical approach helps in understanding how any composite number can be broken down into its fundamental building blocks – the prime numbers.