Rewrite 28 and 72 as product of their prime factors
The correct answer and explanation is:
To express 28 and 72 as a product of their prime factors, the goal is to break down each number into its prime components.
Prime Factorization of 28:
- Start by dividing 28 by the smallest prime number, which is 2. 28÷2=1428 ÷ 2 = 14
- Now divide 14 by 2 again: 14÷2=714 ÷ 2 = 7
- Since 7 is a prime number, the factorization ends here. Thus, the prime factorization of 28 is: 28=2×2×7=22×728 = 2 × 2 × 7 = 2^2 × 7
Prime Factorization of 72:
- Begin by dividing 72 by 2: 72÷2=3672 ÷ 2 = 36
- Divide 36 by 2: 36÷2=1836 ÷ 2 = 18
- Divide 18 by 2 again: 18÷2=918 ÷ 2 = 9
- 9 is not divisible by 2, so move to the next smallest prime, which is 3: 9÷3=39 ÷ 3 = 3
- Finally, divide 3 by 3: 3÷3=13 ÷ 3 = 1
- Now, you have the complete prime factorization of 72, which is: 72=2×2×2×3×3=23×3272 = 2 × 2 × 2 × 3 × 3 = 2^3 × 3^2
Summary:
- The prime factorization of 28 is 22×72^2 × 7.
- The prime factorization of 72 is 23×322^3 × 3^2.
Prime factorization involves breaking a number down into its smallest prime numbers that, when multiplied together, result in the original number. This process is useful for simplifying fractions, finding greatest common divisors, and understanding the number’s divisibility properties.