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Factors and Multiples - Even and Odd Numbers

Grade 4ICSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Factors are numbers that divide a given number completely without leaving a remainder. For example, the factors of 1010 are 1,2,5,1, 2, 5, and 1010. You can visualize this by imagining 1010 marbles; you can arrange them into 22 equal rows of 55 or 11 row of 1010 without any marbles left over.

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Multiples are the products obtained when a number is multiplied by other whole numbers like 1,2,3,1, 2, 3, and so on. Imagine a number line where a grasshopper starts at 00 and jumps 33 units at a time; it will land on 3,6,9,12...3, 6, 9, 12... which are all multiples of 33.

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Even Numbers are numbers that are exactly divisible by 22 and always end with the digits 0,2,4,6,0, 2, 4, 6, or 88 in the ones place. Think of even numbers as 'friendly' numbers where every single item can be grouped into a pair with nothing left alone.

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Odd Numbers are numbers that leave a remainder of 11 when divided by 22 and always end with the digits 1,3,5,7,1, 3, 5, 7, or 99 in the ones place. If you try to group an odd number of items into pairs, there will always be one single item left without a partner.

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A Factor Pair is a set of two numbers which, when multiplied together, give a specific product. For the number 1212, the factor pairs are (1,12)(1, 12), (2,6)(2, 6), and (3,4)(3, 4). You can visualize factor pairs as the length and width of different rectangles that can be formed using the same number of square tiles.

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Common Multiples are numbers that are multiples of two or more different numbers. For example, the multiples of 22 are 2,4,6,8,10,12...2, 4, 6, 8, 10, 12... and the multiples of 33 are 3,6,9,12...3, 6, 9, 12.... The numbers 66 and 1212 are common multiples because they appear in both lists.

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Every number (except 11) has at least two factors: 11 and the number itself. The smallest factor of any number is always 11, and the largest factor is the number itself. On the other hand, a number can have an infinite number of multiples.

📐Formulae

Even Number+Even Number=Even Number\text{Even Number} + \text{Even Number} = \text{Even Number}

Odd Number+Odd Number=Even Number\text{Odd Number} + \text{Odd Number} = \text{Even Number}

Even Number+Odd Number=Odd Number\text{Even Number} + \text{Odd Number} = \text{Odd Number}

Even Number×Any Number=Even Number\text{Even Number} \times \text{Any Number} = \text{Even Number}

Factor×Factor=Multiple\text{Factor} \times \text{Factor} = \text{Multiple}

Number÷Factor=Quotient with Remainder 0\text{Number} \div \text{Factor} = \text{Quotient with Remainder } 0

💡Examples

Problem 1:

Find all the factors of 2020 and list its first five multiples.

Solution:

Step 1: To find factors, check which pairs multiply to 2020: 1×20=201 \times 20 = 20, 2×10=202 \times 10 = 20, 4×5=204 \times 5 = 20. Factors are 1,2,4,5,10,201, 2, 4, 5, 10, 20. \Step 2: To find the first five multiples, multiply 2020 by 1,2,3,4,1, 2, 3, 4, and 55: 20×1=2020 \times 1 = 20, 20×2=4020 \times 2 = 40, 20×3=6020 \times 3 = 60, 20×4=8020 \times 4 = 80, 20×5=10020 \times 5 = 100.

Explanation:

Factors are divisors of 2020, while multiples are the products of 2020 and consecutive counting numbers.

Problem 2:

Identify whether the sum of 156156 and 289289 is Even or Odd without calculating the actual total.

Solution:

Step 1: Check the last digit of 156156. It is 66, so 156156 is an Even number. \Step 2: Check the last digit of 289289. It is 99, so 289289 is an Odd number. \Step 3: Apply the rule Even+Odd=Odd\text{Even} + \text{Odd} = \text{Odd}. \Conclusion: The sum of 156156 and 289289 is an Odd number.

Explanation:

The parity (even or odd) of a sum depends on the parity of the addends. Since one is even and one is odd, the result must be odd.