Give the prime factorization of 136 and (using division method
The correct answer and explanation is:
To find the prime factorization of 136 using the division method, follow these steps:
- Start with the smallest prime number (2):
- 136 is even, so divide it by 2.
- 136÷2=68136 ÷ 2 = 68
- Divide 68 by 2 again:
- 68 is still even, so divide by 2.
- 68÷2=3468 ÷ 2 = 34
- Divide 34 by 2:
- 34 is also even, so divide by 2.
- 34÷2=1734 ÷ 2 = 17
- Check if 17 is divisible by 2:
- 17 is odd, so it is not divisible by 2. Move to the next smallest prime, which is 3.
- Check divisibility by 3:
- The sum of the digits of 17 is 8 (1 + 7), which is not divisible by 3, so 17 is not divisible by 3.
- Check divisibility by 5:
- Since 17 does not end in 0 or 5, it is not divisible by 5.
- Check divisibility by 7:
- 17÷717 ÷ 7 does not result in a whole number, so 17 is not divisible by 7.
- Conclusion:
- 17 is a prime number because it cannot be divided evenly by any prime number less than or equal to its square root (which is approximately 4.1).
Thus, the prime factorization of 136 is: 136=2×2×2×17136 = 2 \times 2 \times 2 \times 17
Or written as: 136=23×17136 = 2^3 \times 17
Explanation:
Prime factorization involves dividing the number by prime numbers in successive steps until the quotient is itself a prime number. For 136, we started by dividing by 2 since it is even and continued dividing by 2 until we reached 17, which is prime. The process ensures that all factors are prime, providing the correct prime factorization.