Question

Which terms could have a greatest common factor of 5m2n2? Check all that apply.m5n55m4n310m4n15m2n224m3n4

Answer 1

5m⁴n³, and

10m⁴n¹⁵

Step-by-step explanation:

Answer 2

The second and the third terms from the choices:

• 5m⁴n³, and
• 10m⁴n¹⁵

Step-by-step explanation:

The greatest common factor of a set of numbers is found by:

1) Write each number as a product of prime factors, each factor raised to the corresponding exponent (power);

2) Choose only the common prime factors, with the least exponent.

Example: find the greatest common factor of 35x²y³ and 15xy²

• Prime factorization: 35x²y³ = 5¹ . 7¹ . x² . y³

15xy² = 3¹ . 5¹ . x¹ . y²

• Common factors (each raised to its least exponent): 5¹, x¹, and y²

• Greatest common factor (make the product): 5 . x . y² = 5xy²

Now apply the process to the given terms:

• m⁵n⁵ : these are prime factors

• 5m⁴n³: these are prime factors

• 10m⁴n¹⁵: prime factors = 2 . 5 . m⁴ n¹⁵

.

• m²n²: these are prime factors

• 24m³n⁴: prime factors = 2³ . 3 . m³ n⁴

The terms that could have a greatest common factor of 5m²n², are those that include 5m²n², and those are:

• 5m⁴n³, and

• 2 . 5 . m⁴ n¹⁵ = 10m⁴n¹⁵

These are the second and the third terms from the choices.