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1 PRIME FACTORIZATION

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2 Every composite number can be expressed as a product of prime numbers. This is called the prime factorization of a number.

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3 PRIME FACTORIZATION To find the prime factorization of a number, you can use a factor tree.

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4 FACTOR TREES 36 6 x 6 ^ ^ 2 x 3 ^ 36 = 2 x 2 x 3 x 3 or 2 ² x 3²3²

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5 FACTOR TREES 36 3 x 12 ^ ^ 3 x 4 36 = 2 x 2 x 3 x 3 2 x 2 ^ or 2 ² x 3²3²

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6 FACTOR TREES 9 3 x 3 ^ 9 = 3 x 3 or 3²3²

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7 FACTOR TREES 21 3 x 7 ^ 21 = 3 x 7

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8 FACTOR TREES 100 10 x 10 ^ ^ 2 x 5 ^ 100 = 2 x 2 x 5 x 5 or 2 ² x 5²5²

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9 PRIME FACTORIZATION To find the prime factorization of a number, you can use a factor ladder.

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10 FACTOR LADDERS 36 18 36 = 2 x 2 x 3 x 3 or 2 ² x 3²3² Begin with the least prime number that is a factor. Repeat until the quotient is prime. 2 2 3 3 9

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11 FACTOR LADDERS 60 30 60 = 2 x 2 x 3 x 5 or 2 ² x 3 x 5 Begin with the least prime number that is a factor. Repeat until the quotient is prime. 2 2 3 5 15

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12 FACTOR LADDERS 45 15 45 = 3 x 3 x 5 or 3 ² x 5 Begin with the least prime number that is a factor. Repeat until the quotient is prime. 3 3 5

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13 FACTOR LADDERS 125 25 125 = 5 x 5 x 5 or 5³ Begin with the least prime number that is a factor. Repeat until the quotient is prime. 5 5 5

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