Question

491400 =

• A. \( 2^3 \times 3^3 \times 5^3 \times 7 \times 13 \)
• B. \( 2^3 \times 3^3 \times 5^2 \times 7 \times 13 \)
• C. \( 2^3 \times 3^2 \times 5^2 \times 7 \times 13 \)
• D. \( 2^2 \times 3^2 \times 5^2 \times 7 \times 13 \)

Hint:

To factorize large numbers, start with the smallest primes and divide repeatedly until no longer divisible. Then continue with larger primes.

Answer 1

The Correct Option is B

Step 1: Factorize the number 491400
- To factorize 491400, we begin by dividing by prime numbers: \[ 491400 \div 2 = 245700 \] \[ 245700 \div 2 = 122850 \] \[ 122850 \div 2 = 61425 \quad (\text{Now no longer divisible by 2, move to the next prime}) \] \[ 61425 \div 3 = 20475 \] \[ 20475 \div 3 = 6825 \] \[ 6825 \div 3 = 2275 \] \[ 2275 \div 5 = 455 \] \[ 455 \div 5 = 91 \] \[ 91 \div 7 = 13 \] Step 2: Express the prime factors
- The prime factorization of 491400 is: \[ 491400 = 2^3 \times 3^3 \times 5^2 \times 7 \times 13 \] Step 3: Conclusion
Thus, the correct factorization is option \( (2) \).