Prime Factorization examples and questions , with detailed solutions and explanations, for grade 6 students are presented. A review of factors and multiples would be very helpful to understand prime factorization. ## Prime NumbersDefinition: Any whole number that can be divided by 1 and itself ONLY is called a prime number.
2 is a prime number, why? 2 can be divided by 1 2 ÷ 1 = 2 with remainder equal to zero 2 can be divided by 2 (itself) 2 ÷ 2 = 1 with remainder equal to zero Try to find another whole number that divides 2 with remainder zero. There is not.
7 is a prime number, why? 7 can be divided by 1 7 ÷ 1 = 7 with remainder equal to zero 7 can be divided by 7 (itself) 7 ÷ 7 = 1 with remainder equal to zero Try to find another whole number that divides 7 with remainder zero. There is not. The first 10 prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 You can generate more prime numbers and test them. ## Composite NumbersDefinition: Any whole number that can be divided (with remainder equal to zero) by another whole number other than 1 and itself is called composite number. 4 is a composite number, why?
4 can be divided by 1, itself and 2.
6 is a composite number, why?
6 can be divided by 1, itself, 2 and 3.
12 is a composite number : it can be divided by 1, itself, 2, 3, 4 and 6. 30 is a composite number: it can be divided by 1, itself, 2, 3, 5, 6, 10 and 15.
## FactorizationFrom division to multiplication to factoring. Division and multiplication are related operations. The division 6 ÷ 3 = 2 may be written as a multiplication: 6 = 2 × 3
Examples 1) 6 = 1 × 6 ; 6 = 2 × 3 1, 2, 3 and 6 are called factors of 6. 2) 12 = 12 ×1 = 3 ×4 = 6 ×2 1, 2, 3, 4, 6 and 12 are called factors of 12. 3) 20 = 1 × 20 = 2 ×10 = 2 × 2 × 5 = 4 × 5 1, 2, 3, 4, 5, 10 and 20 are called factors of 20. ## Prime factorization
Examples 1) 6 = 2 × 3 the factors 2 and 3 are prime numbers. 2) 12 = 2 × 2 × 3 the factors 2 and 3 are prime numbers. 3) 20 = 2 × 2 × 5 the factors 2 and 5 are prime numbers.
Write the prime factorization of 12 1) See if the first prime number 2 is a factor of the given number 12 12 ÷ 2 = 6 with remainder = 0 2 is a factor of 12 12 = 2 × 6 2) See if the first prime number 2 is a factor of 6 6 ÷ 2 = 3 with remainder = 0 2 is a factor of 6 6 = 2 × 3 Hence 12 = 2 × 6 = 2 × 2 × 3 12 = 2 × 2 × 3 is completely factored using only prime numbers 2 and 3
Write the prime factorization of 21 1) See if the first prime number 2 is a factor of the given number 21 21 ÷ 2 = 10 but remainder = 1 so 2 is not a factor of 21 2) Is the next prime number 3 a factor of 21? 21 ÷ 3 = 7 with remainder 0 3 is a factor of 21 21 = 3 × 7 3 and 7 are prime numbers and therefore 21 = 3 × 7 is completely factored using only prime numbers 3 and 7 This prime factor calculator can be used to generate all prime factors of a given number. |

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