Multiples of 3

Answer: Multiples of 3 are numbers that can be divided by 3 with no remainder. They are the results of multiplying 3 by any integer. Examples include 0, 3, 6, 9, 12, 15, 18, 21, and so on. They can also be negative, such as -3, -6, -9.

Explanation: In mathematics, a multiple of a number is the product of that number and any integer (..., -2, -1, 0, 1, 2, ...). When we talk about 'multiples of 3', we are referring to any number that can be obtained by multiplying 3 by an integer.

To find multiples of 3, you simply multiply 3 by a sequence of integers:

   3 × 0 = 0

   3 × 1 = 3

   3 × 2 = 6

   3 × 3 = 9

   3 × 4 = 12

   3 × 5 = 15

  and so on for positive integers.

Multiples can also be negative:

   3 × -1 = -3

   3 × -2 = -6

   3 × -3 = -9

   and so on for negative integers.

Key characteristics of multiples of 3:

1.  Divisibility: Every multiple of 3 is perfectly divisible by 3, meaning when divided by 3, the remainder is 0.

2.  Sum of Digits: A common divisibility rule states that a number is a multiple of 3 if the sum of its digits is a multiple of 3. For example, for the number 123, the sum of its digits is 1+2+3=6. Since 6 is a multiple of 3, 123 is also a multiple of 3 (123 = 3 × 41).

3.  Arithmetic Sequence: When listed in order, multiples of 3 form an arithmetic progression with a common difference of 3 (e.g., ..., -6, -3, 0, 3, 6, 9, ...).

Understanding multiples is a fundamental concept in arithmetic, crucial for topics like fractions, common denominators, and factorization.