Find the GCF of 30m + 12n .(1 point)
To find the greatest common factor (GCF) of the terms in the expression 30m + 12n, we need to find the largest integer that divides both coefficients (30 and 12) and any common variables.
Since there are no common variables between 30m and 12n (the variable m is only in the first term, and n is only in the second), we only need to focus on the coefficients.
The GCF of 30 and 12 is found by considering the prime factorization of both numbers:
- The prime factorization of 30 is 2 × 3 × 5.
- The prime factorization of 12 is 2 × 2 × 3.
The GCF is the product of the common prime factors in both numbers, counting each prime factor the least times it appears in either factorization.
In this case, the common prime factors are 2 and 3. However, since the exponent of 2 in the factorization of 12 is 2 (meaning 12 has two factors of 2), and in the factorization of 30, it's only 1 (only one factor of 2), we take the lower count, which is 1.
Therefore, the GCF of 30 (2 × 3 × 5) and 12 (2 × 2 × 3) is 2 × 3 = 6.
The GCF of 30m + 12n is 6.