The greatest common factor (GCF) of 42, 126, and 210 is 42.
To find the GCF, we first need to look at the prime factorization of each number:
- 42 = 2 × 3 × 7
- 126 = 2 × 3² × 7
- 210 = 2 × 3 × 5 × 7
Next, we identify the common factors in these factorizations. The common prime factors of these numbers are:
- 2
- 3
- 7
To calculate the GCF, we take the lowest power of each common prime factor:
- 2 (power of 1)
- 3 (power of 1)
- 7 (power of 1)
Now we multiply these together:
GCF = 21 × 31 × 71 = 2 × 3 × 7 = 42.
Therefore, 42 is the greatest common factor of 42, 126, and 210.