Factors and Common Factors

A factor of a number is any number that divides the given number completely without leaving a remainder.

or

When two numbers are multiplied, the result is called their product, and the numbers that are multiplied are called factors of the product.

A product is the result of multiplying two or more constants or literals (letters) or both.

• Example:
  5xy is a product of 5, x, and y.

• Each number or letter multiplied in a product is called a factor.
  So, in 5xy, the factors are 5, x, and y.

1.12 is exactly divisible by 1, 2, 3, 4, 6, and 12, which means the remainder is 0. These numbers are called divisors or factors of 12

2. Factors of 24:
24 = 1 × 24,
24 = 2 × 12,
24 = 3 × 8,
24 = 4 × 6
So, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.

3. Factors of 30:
1, 2, 3, 5, 6, 10, 15, 30.

4. Factors of 18:
1, 2, 3, 6, 9, 18.

5. Factors of 45:
1, 3, 5, 9, 15, 45.

• 1 is a factor of every number.
• Every number is a factor of itself.
• Zero (0) is not a factor of any number.
• Every factor of a number is an exact divisor of that number.
• Every factor is less than or equal to the given number.
• The number of factors of a given number is finite.

A common factor of two or more numbers is a number that divides each of the given numbers exactly, without leaving any remainder.

Activity: Jump Jackpot Game (Understanding Common Factors)

Objective:

• To understand common factors using a fun jumping game.
• To learn how to identify numbers that divide both given numbers exactly.

Steps:
1. Set up the game

• Grumpy places a treasure on a number (e.g., 24).
• Jumpy picks a jump size (e.g., 4) and jumps in multiples of that number (e.g., 0, 4, 8, 12, 16, 24).

2. Jumpy’s Jumping:

• Jumpy starts at 0 and jumps in multiples of his chosen number.
• He lands on the treasure if he reaches the number where Grumpy placed it.

3. Example 1: Jumping on 24

• Jumpy uses jump size 4 and lands on 24.
• The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.

4. Example 2: Multiple Treasures:

• Grumpy places treasures on 14 and 36.
• Jumpy uses jump size 7 and lands on 14 but not 36.
• The common factors of 14 and 36 are 1 and 2.

Conclusion:

• Common factors are the numbers that divide two numbers exactly.
• In the game, we found the common factors by using different jump sizes and seeing where Jumpy lands