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Divisors and Factors

  • Closure Property of whole numbers:
    • Whole numbers are closed under addition. For example, the sum of whole numbers 3 and 8 is 11 (3 + 8 = 11), which is again a whole number.
    • Whole numbers are closed under multiplication. For example, the multiplication of whole numbers 4 and 7 is 28 (4 × 7 = 28), which is again a whole number.
    • Whole numbers are not closed under subtraction. For example, 5 – 2 = 3 is a whole number, but 1 – 2 =  –1 is not a whole number.
    • Whole numbers are not closed under division. For example, 98 ÷ 4 = 2 is a whole number, but 2 ÷ 5 =  is not a whole number.

 

  • Properties of whole numbers:

We can add or multiply two whole numbers in any order, that is, 12 + 5 = 5 + 12 = 17 and 9 × 8 = 8 × 9 = 72.

This property of addition and multiplication of whole numbers is known as commutative.

Addition and multiplication of whole numbers are associative.

 For example: (17 + 19) + 25 = 17 + (19 + 25) = 61.

Similarly, (6 × 13) × 19 = 6 × (13 × 19) = 1482.

These properties help some mathematical calculations easier.

 

Example: Find the value of 4 × 17 × 25.

Solution:

4 × 17 × 25 = 4 × 25…

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