To find the greatest common factor (GCF) of 99 and 45, we can start by determining the prime factorizations of both numbers.
Step 1: Prime factorization of 99
- \(99 = 3 \times 33\)
- \(33 = 3 \times 11\)
- Thus, the prime factorization of 99 is \(3^2 \times 11\).
Step 2: Prime factorization of 45
- \(45 = 5 \times 9\)
- \(9 = 3 \times 3 = 3^2\)
- Thus, the prime factorization of 45 is \(3^2 \times 5\).
Step 3: Identify the common prime factors
- The common prime factor is \(3\).
Step 4: Determine the minimum exponent of the common prime factor
- For 99, the exponent of 3 is \(2\).
- For 45, the exponent of 3 is \(2\).
- The minimum exponent is \(2\).
Step 5: Calculate the GCF
- Therefore, the GCF is \(3^2 = 9\).
Thus, the greatest common factor of 99 and 45 is 9.
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