Math / Numbers & Operations

QuestionList the first 5 multiples, and find ALL the factors of 21.
Multiples:
Factors: Prime or Composite?

Studdy Solution

STEP 1

1. A multiple of a number is the product of that number and an integer.
2. A factor of a number is an integer that divides the number without leaving a remainder.
3. We need to list the first 5 multiples of 21.
4. We need to find all factors of 21.
5. We need to determine if 21 is a prime or composite number.

STEP 2

1. List the first 5 multiples of 21.
2. Find all factors of 21.
3. Determine if 21 is prime or composite.

STEP 3

To find the first 5 multiples of 21, multiply 21 by the first 5 positive integers.
$21 \times 1 = 21$ $21 \times 2 = 42$ $21 \times 3 = 63$ $21 \times 4 = 84$ $21 \times 5 = 105$
The first 5 multiples of 21 are: $21, 42, 63, 84, 105$ .

STEP 4

To find all factors of 21, determine which integers divide 21 without leaving a remainder.
Check divisibility by integers starting from 1 up to $\sqrt{21}$ .
$21 \div 1 = 21 \quad (\text{remainder } 0)$ $21 \div 3 = 7 \quad (\text{remainder } 0)$ $21 \div 7 = 3 \quad (\text{remainder } 0)$ $21 \div 21 = 1 \quad (\text{remainder } 0)$
The factors of 21 are: $1, 3, 7, 21$ .

STEP 5

Determine if 21 is prime or composite.
A prime number has exactly two distinct positive divisors: 1 and itself. A composite number has more than two positive divisors.
Since 21 has four factors: $1, 3, 7, 21$ , it is a composite number.
Multiples: $21, 42, 63, 84, 105$
Factors: $1, 3, 7, 21$
Prime or Composite? Composite

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