Question

greatest common factor - item 34685 question 2 of 3 juanita wants to rewrite 48 + 18 using the greatest common factor and the distributive property. complete the statements below. the greatest common factor of 48 and 18 is blank. juanita can use the greatest common factor to rewrite 48 + 18 as blank(8 + blank).

Explanation:

Step1: Find factors of 48 and 18

Factors of 48: \(1, 2, 3, 4, 6, 8, 12, 16, 24, 48\)
Factors of 18: \(1, 2, 3, 6, 9, 18\)
Common factors: \(1, 2, 3, 6\). Greatest common factor (GCF) is \(6\).

Step2: Rewrite \(48 + 18\) using GCF

Divide 48 by 6: \(\frac{48}{6} = 8\)
Divide 18 by 6: \(\frac{18}{6} = 3\)
Using distributive property \(a(b + c)=ab + ac\), reverse: \(ab + ac = a(b + c)\). So \(48 + 18 = 6(8 + 3)\).

Answer:

The greatest common factor of 48 and 18 is \(\boldsymbol{6}\).
Juanita can use the greatest common factor to rewrite \(48 + 18\) as \(\boldsymbol{6}(8 + \boldsymbol{3})\).