(a) find the gcf of 42 and 35
Gcf = ?
(b) use the gcf to factor 42-35
42-35=?x(?+?)
(a) To find the greatest common factor (GCF) of 42 and 35, we'll look for the largest number that divides both numbers.
Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
Factors of 35: 1, 5, 7, 35
The largest number that appears in both lists is 7, so the GCF of 42 and 35 is 7.
GCF = 7
(b) Now, using the GCF to factor the expression 42 - 35, we express both numbers as multiples of their GCF and then factor out the common factor.
42 = 7 * 6
35 = 7 * 5
42 - 35 = 7 * 6 - 7 * 5
Factoring out the common factor of 7, we get:
7 * (6 - 5)
Since (6 - 5) is equal to 1, the expression simplifies to:
7 * 1 or simply 7
So, 42 - 35 is equal to 7, and when factored using the GCF, it is 7 * (6 - 5) or just 7.