The product of a multiplication problem being 144 means that 144 can be expressed as the product of two or more factors. Here are a few key points about the factors of 144:
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Factor Pairs: The factors of 144 are numbers that can be multiplied together to yield 144. Some of the factor pairs are:
- \(1 \times 144\)
- \(2 \times 72\)
- \(3 \times 48\)
- \(4 \times 36\)
- \(6 \times 24\)
- \(8 \times 18\)
- \(9 \times 16\)
- \(12 \times 12\)
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Prime Factorization: The prime factorization of 144 is: \[ 144 = 12 \times 12 = (2^2 \times 3) \times (2^2 \times 3) = 2^4 \times 3^2 \] This shows that the prime factors of 144 are 2 and 3.
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Number of Factors: To determine the total number of factors, you can use the formula based on prime factorization. For \(144 = 2^4 \times 3^2\), the exponents are 4 and 2. To find the number of factors, you add 1 to each of the exponents and then multiply: \[ (4 + 1)(2 + 1) = 5 \times 3 = 15 \] Therefore, 144 has a total of 15 factors.
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Perfect Square: 144 is a perfect square because it can be expressed as \(12^2\).
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Divisibility: 144 is even and thus divisible by 2. It is also divisible by 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, and 72.
In summary, the factors of 144 can be found through factor pairs, the prime factorization reveals its constituent primes, and it has 15 factors in total, making it a perfect square.
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