Give the prime factorization of 136 and 56 (using division method)
The correct answer and explanation is:
Let’s find the prime factorization of 136 and 56 using the division method.
Prime Factorization of 136:
- Start by dividing 136 by the smallest prime number, which is 2: 136÷2=68136 \div 2 = 68
- Divide 68 by 2 again: 68÷2=3468 \div 2 = 34
- Divide 34 by 2 once more: 34÷2=1734 \div 2 = 17
- 17 is a prime number, so stop here.
The prime factorization of 136 is: 136=2×2×2×17=23×17136 = 2 \times 2 \times 2 \times 17 = 2^3 \times 17
Prime Factorization of 56:
- Start by dividing 56 by 2: 56÷2=2856 \div 2 = 28
- Divide 28 by 2 again: 28÷2=1428 \div 2 = 14
- Divide 14 by 2 once more: 14÷2=714 \div 2 = 7
- 7 is a prime number, so stop here.
The prime factorization of 56 is: 56=2×2×2×7=23×756 = 2 \times 2 \times 2 \times 7 = 2^3 \times 7
Explanation:
The division method is a step-by-step process where we divide the given number by the smallest prime number until we cannot divide anymore. In both cases, we started by dividing by 2, the smallest prime, and continued until we reached a prime number. The final result is the prime factorization, where the original number is written as a product of prime numbers raised to appropriate powers.
For 136, we divided it three times by 2 and then by 17. For 56, we divided it three times by 2 and then by 7. This method ensures that we break down the number into its prime components.