A number is a ____ of each of its factor.
multiple
Idea: If a number a is a factor of a number N, then N can be made by multiplying a with some whole number.
Meaning of factor: A number a is a factor of N if it divides N exactly (no remainder).
So, if a is a factor of N, we can write:
\( N = a \times k \)
for some whole number \( k \).
Meaning of multiple: A number is a multiple of a if it can be written as
\( a \times \, ext{(some whole number)} \).
Comparing both statements:
\( N = a \times k \Rightarrow N \) is a multiple of \( a \).
Example:
Take \( N = 12 \).
Factors of \( 12 \) are: \( 1, 2, 3, 4, 6, 12 \).
\( 12 = 1 \times 12 \Rightarrow 12 \) is a multiple of \( 1 \).
\( 12 = 2 \times 6 \Rightarrow 12 \) is a multiple of \( 2 \).
\( 12 = 3 \times 4 \Rightarrow 12 \) is a multiple of \( 3 \).
\( 12 = 4 \times 3 \Rightarrow 12 \) is a multiple of \( 4 \).
\( 12 = 6 \times 2 \Rightarrow 12 \) is a multiple of \( 6 \).
\( 12 = 12 \times 1 \Rightarrow 12 \) is a multiple of \( 12 \).
Conclusion: A number is a multiple of each of its factors.