Find the GCF of 30m + 12n .(1 point)
The Greatest Common Factor (GCF) of 30m and 12n is 6.
To find the greatest common factor (GCF) of 30m and 12n, you can start by factoring each term completely.
For 30m:
The prime factorization of 30 is 2 * 3 * 5.
The prime factorization of m is just m.
Therefore, the prime factorization of 30m is 2 * 3 * 5 * m.
For 12n:
The prime factorization of 12 is 2 * 2 * 3.
The prime factorization of n is just n.
Therefore, the prime factorization of 12n is 2 * 2 * 3 * n.
To find the GCF, you need to find the highest power of each common prime factor.
The common prime factors between 30m and 12n are 2 and 3.
The highest power of 2 in 30m is 2^1.
The highest power of 2 in 12n is 2^2.
Therefore, the GCF contains 2^1.
The highest power of 3 in 30m is 3^1.
The highest power of 3 in 12n is 3^1.
Therefore, the GCF contains 3^1.
Putting it all together, the GCF of 30m and 12n is 2 * 3, which equals 6.
Therefore, the GCF of 30m and 12n is 6.
To find the Greatest Common Factor (GCF) of 30m + 12n, we can factor out any common factors from both terms.
First, let's look at the coefficients of the terms 30m and 12n. The GCF of 30 and 12 is 6. This means we can factor out a 6 from both terms.
Next, let's look at the variables in both terms. In this case, we have m in the first term and n in the second term. Since there is no common variable between the two terms, we cannot factor out any variables.
Combining the GCF of the coefficients (6) with the variables (m and n), the GCF of 30m and 12n is 6.
Therefore, the GCF of 30m + 12n is 6.