Question

Haley and Maddie both pick a number. Haley's number has a prime factorization with 3 numbers. Maddie's number has a prime factorization with 6 numbers. Maddie says that her number must be bigger than Haley's because she has 6 numbers in her prime (factorization and Haley only has 3. Haley sald that is not necessarily true. Who is correct?

Answer 1

Explanation:

Maddie is incorrect in assuming that her number must be bigger than Haley's because she has 6 numbers in her prime factorization compared to Haley's 3. The number of factors in the prime factorization does not determine the size or magnitude of the number.

The prime factorization of a number is the expression of that number as a product of prime numbers. For example, if Haley's number is 2 * 3 * 5 = 30, then her prime factorization has 3 numbers: 2, 3, and 5.

If Maddie's number is 2 * 2 * 3 * 5 * 7 * 11 = 4620, then her prime factorization has 6 numbers: 2, 2, 3, 5, 7, and 11.

The number of prime factors does not indicate the size of the number. It is possible for a number with fewer prime factors to be larger than a number with more prime factors. For example, 30 (Haley's number) is smaller than 4620 (Maddie's number), even though Haley has 3 prime factors and Maddie has 6 prime factors.

Therefore, Haley is correct in stating that the number of prime factors does not necessarily determine the size of the number.