#1
What is the Greatest Common Factor (GCF) of 12 and 18?
3
Explanation3 is the largest number that divides both 12 and 18.
#2
Determine the GCF of 16 and 24.
4
ExplanationThe largest number that divides both 16 and 24 is 4.
#3
What is the GCF of 40 and 60?
20
ExplanationThe largest number that divides both 40 and 60 is 20.
#4
Find the GCF of 84 and 105.
21
ExplanationThe largest number that divides both 84 and 105 is 21.
#5
What is the GCF of 32 and 48?
8
ExplanationThe largest number that divides both 32 and 48 is 8.
#6
Factorize the polynomial x^2 - 4x + 4.
(x - 2)^2
ExplanationThe expression factors to (x - 2)(x - 2) or (x - 2)^2.
#7
Find the GCF of 24, 36, and 48.
12
ExplanationThe largest number that divides all three numbers, 24, 36, and 48, is 12.
#8
Factorize the expression 3x^2 - 12x + 12.
3(x - 2)^2
ExplanationThe expression factors to 3(x - 2)(x - 2) or 3(x - 2)^2.
#9
Find the GCF of 54 and 72.
6
ExplanationThe largest number that divides both 54 and 72 is 6.
#10
Factorize the trinomial 2x^2 - 11x + 15.
(2x - 3)(x - 5)
ExplanationThe expression factors to (2x - 3)(x - 5).
#11
Determine the GCF of 63 and 81.
9
ExplanationThe largest number that divides both 63 and 81 is 9.
#12
Factorize the quadratic expression 2x^2 - 8x + 8.
2(x + 2)^2
ExplanationThe expression factors to 2(x + 2)(x + 2) or 2(x + 2)^2.
#13
What is the GCF of 36 and 48 expressed in prime factorization?
2^2 * 3
ExplanationThe prime factorization of 36 is 2^2 * 3^2 and the prime factorization of 48 is 2^4 * 3. The GCF is the product of the common prime factors, which is 2^2 * 3.
#14
Factorize the polynomial 4x^2 - 25.
(2x - 5)(2x + 5)
ExplanationThe expression factors to (2x - 5)(2x + 5).
#15
Factorize the expression x^3 - 8.
(x - 2)(x^2 - 2x + 4)
ExplanationThe expression factors to (x - 2)(x^2 - 2x + 4).
#16
Factorize the expression 6x^2 - 27.
3(2x - 3)(2x + 3)
ExplanationThe expression factors to 3(2x - 3)(2x + 3).
#17
What is the GCF of 72 and 120 expressed in prime factorization?
2^2 * 3^2 * 5
ExplanationThe prime factorization of 72 is 2^3 * 3^2 and the prime factorization of 120 is 2^3 * 3 * 5. The GCF is the product of the common prime factors, which is 2^2 * 3 * 5.