Decomposing a Number into Prime Factors

Learning Goals We will use our divisibility rules so that we can decompose numbers into prime factors. We’ll know we understand when we can identify the prime factors that are used to form a number.

Vocabulary Composite number Divisibility Division Divisor Factor / Prime factor Prime number

Use Your Divisibility Rules A number is divisible by 2 if the last digit is even (0, 2, 4, 6, or 8) A number is divisible by 3 if the sum of all the digits in the number is divisible by 3. A number is divisible by 5 if the last digit is 0 or 5. A number is divisible by 10 if the last digit is 0.

Use Your Divisibility Rules A number is divisible by 4 if the last 2 digits are both 0 or if they are divisible by 4 or 2 twice. A number is divisible by 6 if it is divisible by 2 and by 3 (i.e. if it ends in an even number and if the sum of its digits is divisible by 3). A number is divisible by 8 if the last 3 digits are all 0 or if the number they form is divisible by 4. A number is divisible by 9 if the sum of its digits is divisible by 9.

Decomposing a Number into Prime Factors A decomposed (or factorized) number means that it is only represented by prime numbers. Use your divisibility rules to help you find the prime factorization of a number. A number’s factors are also its divisors. Remember: a prime number has only 2 divisors – 1 and itself (i.e. 2, 5, 23, etc.) The divisors of 64 are {1, 2, 4, 8, 16, 32, 64}. 2 is its only prime factor.

Decomposing a Number into Prime Factors 1.Find 2 factors of the number to be decomposed. 2.If any of these are prime numbers, move on to the next number. 3.Reduce all numbers to prime factors. 4.Always remember to use exponents to represent prime factors that appear more than once. 5.Always remember to arrange your factors in increasing order x74 2 x 5x 2 x = 2 2 x 5 x 37