Prime Time

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A factor of a number is a number that divides it exactly (with remainder 0). For example, the factors of 12 are 1, 2, 3, 4, 6, and 12 because each of these numbers divides 12 exactly.

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A multiple of a number is obtained by multiplying that number by any whole number. For example, multiples of 5 are 5, 10, 15, 20, 25, 30... (5×1, 5×2, 5×3, 5×4, 5×5, 5×6...)

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Players say 'idli-vada' when the number is a multiple of both 3 and 5. The first such number is 15, then 30, 45, 60, 75, 90... These are called common multiples of 3 and 5.

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Common factors are numbers that divide two or more numbers exactly. Factors of 14: 1, 2, 7, 14. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Common factors of 14 and 36 are 1 and 2.

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A prime number has exactly two factors: 1 and itself. The first five prime numbers are 2, 3, 5, 7, and 11. Note: 2 is the only even prime number.

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A composite number has more than two factors. Examples: 4 (factors: 1, 2, 4), 6 (factors: 1, 2, 3, 6), and 9 (factors: 1, 3, 9). All composite numbers have at least one factor other than 1 and themsel

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The number 1 is neither prime nor composite. It has only one factor (itself), while prime numbers must have exactly two factors (1 and themselves), and composite numbers must have more than two factor

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The Sieve of Eratosthenes is a method to find all prime numbers up to a given number. Steps: 1) Cross out 1, 2) Circle 2, cross out all its multiples, 3) Circle the next uncrossed number, cross out it