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Notes – Number of the Day prime number – a number whose only factors are itself and 1. Ex: 5 is a prime number. The factors of 5 are 1 and 5. composite number – a number that has more than one proper factor Ex: 10 is a composite number. The factors of 10 are 1,2, and 5. factors - numbers multiplied together to get a product Ex: 1, 2, 5 and 10 are factors of 10. *Factors of a number must be equal to or less than the number. proper factors of a number – all the factors of a number except for the number itself Ex: factors of 10 – 1, 2, 5, 10 proper factors of 10 – 1,2,5 common factor factors that are shared by two or more numbers Ex: factors of 10 – 1, 2, 5, 10 factors of 30 – 1, 2, 3, 5, 6, 10, 15, 30 common factors of 10 and 30 – 1, 2,5, 10 Greatest Common Factor – The largest factor shared by two or more numbers Ex: the GCF of 10 and 30 is 10 multiples of a number – products of that number and another number. Multiples of a number make up the multiplication table for that number. Ex: multiples of 10 – 10, 20, 30, 40… *Multiples of a number must be equal to or greater than the number. common multiples – multiples that are shared by two or more numbers Ex: multiples of 10 – 10, 20, 30, 40… multiples of 5 - 5, 10, 15, 20, 25, 30, 35, 40… common multiples of 10 and 5 – 10, 20, 30, 40… Least Common Multiple – The smallest multiple that is common to two or more numbers Ex: LCM for 10 and 5 is 10. abundant number – any number whose proper factors add up to more than the number itself Ex: 12 is an abundant number. proper factors of 12 – 1, 2, 3, 4, 6, 1 + 2 + 3 + 4 + 6 = 16 16 > 12 deficient number – any number whose proper factors add up to less than the number itself Ex: 10 is a deficient number proper factors of 10 – 1, 2, 5 1+2+5=8 8 < 10 exponent - A small raised number written to the right of a digit that tells how many time that digit is used as a factor factor tree – strategy for finding the prime factorization of a number 270 10 5 X X 2 27 3 X 9 3 X 3 prime factorization – the longest factor string for a number made up of only prime numbers Ex: The prime factorization for 270 is 2 X 3 X 3 X 3 X 5 3 The prime factorization with exponents is 2 X 3 X 5 . The digit 3 is used as a factor three times so we use the exponent 3 . Divisibility rules Divisible by 2 – if there is a 2,4,6,8,or 0 in the ones place Divisible by 3 – if the sum of the digits in the number is a multiple of 3 then the number is divisible by 3. Ex: 1344 is divisible by 3 because the sum of the digits, 1 + 3 + 4 + 4 = 12 and 12 is a multiple of 3. Divisible by 6 – if the number is divisible by 2 and 3 Divisible by 5 – if there is a 0 or 5 in the ones place Divisible by 10 – if there is a 0 in the ones place Using prime factorization to find the GCF Find the GCF for 260 and 36 Make a factor tree for each number to find each prime factorization. PF for 260 = 2 X 2 X 5 X 13 PF for 36 = 2 X 2 X 3 X 3 Make a factor string using only the factors that are shared by both prime factorizations. GCF = 2 X 2 = 4 Using prime factorization to find LCM Find the LCM for 260 and 36 Make a factor tree for each number to find each prime factorization. PF for 260 = 2 X 2 X 5 X 13 PF for 36 = 2 X 2 X 3 X 3 Make the shortest factor string which contains both prime factorizations. LCM = 2 X 2 X 3 X 3 X 5 X 13 = 2340