Question

click a number from the hundreds chart below and state if it is or isnt a factor of 16. if it is a factor, fill in the missing number in the multiplication sentence to find the other factor in the pair.

Explanation:

Step1: Recall factor - definition

A factor of a number divides the number evenly. To check if a number \(n\) is a factor of 16, we see if \(16\div n\) has a remainder of 0.

Step2: Check numbers from the chart

• For \(n = 1\): \(16\div1=16\), so 1 is a factor and the multiplication sentence is \(1\times16 = 16\).
• For \(n = 2\): \(16\div2 = 8\), so 2 is a factor and the multiplication sentence is \(2\times8=16\).
• For \(n = 3\): \(16\div3=\frac{16}{3}=5\frac{1}{3}\), so 3 is not a factor.
• For \(n = 4\): \(16\div4 = 4\), so 4 is a factor and the multiplication sentence is \(4\times4=16\).
• For \(n = 5\): \(16\div5=\frac{16}{5}=3\frac{1}{5}\), so 5 is not a factor.
• For \(n = 6\): \(16\div6=\frac{16}{6}=\frac{8}{3}=2\frac{2}{3}\), so 6 is not a factor.
• For \(n = 7\): \(16\div7=\frac{16}{7}=2\frac{2}{7}\), so 7 is not a factor.
• For \(n = 8\): \(16\div8 = 2\), so 8 is a factor and the multiplication sentence is \(8\times2=16\).
• For \(n = 9\): \(16\div9=\frac{16}{9}=1\frac{7}{9}\), so 9 is not a factor.
• For \(n = 10\): \(16\div10=\frac{16}{10}=\frac{8}{5}=1\frac{3}{5}\), so 10 is not a factor.
• For \(n = 11\): \(16\div11=\frac{16}{11}=1\frac{5}{11}\), so 11 is not a factor.
• For \(n = 12\): \(16\div12=\frac{16}{12}=\frac{4}{3}=1\frac{1}{3}\), so 12 is not a factor.
• For \(n = 13\): \(16\div13=\frac{16}{13}=1\frac{3}{13}\), so 13 is not a factor.
• For \(n = 14\): \(16\div14=\frac{16}{14}=\frac{8}{7}=1\frac{1}{7}\), so 14 is not a factor.
• For \(n = 15\): \(16\div15=\frac{16}{15}=1\frac{1}{15}\), so 15 is not a factor.
• For \(n = 16\): \(16\div16 = 1\), so 16 is a factor and the multiplication sentence is \(16\times1=16\).

Answer:

The factors of 16 from the chart are 1 (with pair - factor 16: \(1\times16 = 16\)), 2 (with pair - factor 8: \(2\times8=16\)), 4 (with pair - factor 4: \(4\times4=16\)), 8 (with pair - factor 2: \(8\times2=16\)), 16 (with pair - factor 1: \(16\times1=16\)). Non - factors are 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15 and all other numbers in the chart not listed as factors.