Question

A) The common factors of 16 and 28 are 1, 2, 4, and 7.
B) The first three common multiples of 4 and 6 are 12, 24, and 36.
State `True' or `False' for both the statements.

Answer 1

Hint: Common factors are factors (divisors) that are in common among a set of numbers.
First, always find out the list of positive integer factors of the given number that divides it without a remainder. Then, check out for the numbers that are common in the given set.
A common multiple is a whole number that is a shared multiple of each set of numbers. The multiples that are common to two or more numbers are called the common multiples of those numbers. First, always find out the list of multiples of 4 and 6 and check out the first three common numbers of 4 and 6.

Complete step-by-step answer:
Factors of 16:
List of positive integers factors of 16 that divides 16 without a remainder are:
\[1,\ 2,\ 4,\ 8,\ 16----(1)\]
Factors of 28:
List of positive integers 28 that divides 28 without a remainder are:
\[1,\ 2,\ 4,\ 7,\ 14,\ 28----(2)\]
By using equation 1 and 2, we get:
The common factors of 16 and 28 are: 1, 2, and 4.

Thus, the given statement `The common factors of 16 and 28 are 1, 2, 4, and 7' is False.

Multiples of 4:
List of multiples of 4 are:
\[\mathrm{4,\ 8,\ 12,\ 16,\ 20,\ 24,\ 28,\ 32,\ 36,\ 40}\mathrm{,\ 44,}\mathrm{\dots }\mathrm{\dots }\mathrm{\ }----(1)\]
Multiples of 6:
List of multiples of 6 are:
\[\mathrm{6,\ 12,\ 18,\ 24,\ 30,\ 36,\ 42,\ 48,\ 54,\ 60,\ 66},\mathrm{\dots }\mathrm{\dots }\mathrm{\ }----(2)\]
By using equation 1 and 2, we get:

The first three common multiples of 4 and 6 are: 12, 24, and 36. Therefore, the statement is true.

Note:
Always for such questions, try to find out the list of positive integer~factors of the given number~that divides it without a remainder and then, list out the factors (i.e. numbers) that are common in the given set. Try to find out the list of multiples of the given number and then, list out the first three factors (i.e. numbers) that are common in the given set..