Name: _______________________ Class: 6________ CN:_______ Parents’ Signature: ______ Number Theory Learning Objective • Shows mastery on the basic concepts of number theory I. Odd and Even Numbers Odd Numbers are counting numbers that are not divisible by two. Examples: The first five odd numbers are 1, 3, 5, 7, and 9. The odd numbers between 40 and 60 are 41, 43, 45, 47, 49, 51, 53, 55, 57 and 59. Even Numbers are counting numbers that are divisible by two. Examples: The first 10 even numbers after 50 are 52, 54, 56, 58, 60, 62, 64, 66, 68, and 70. The even number right before 100 is 98. II. Factors and Multiples Factors are numbers multiplied to get another number as their product. Examples: The factors of 24 are: 1 x 24 3x8 2 x 12 4x6 The factors of 42 are: 1 x 42 3 x 14 2 x 21 6x7 *Greatest Common Factor Greatest common factor (GCF) of a set of numbers is the greatest whole number which is the factor of the given set of numbers. Decomposition/Continuous Division Listing Method GCF of 6, 12, 18 = ? GCF of 6, 12, 18 = ? 2 6 12 18 6 = 1, 2, 3, 6 3 3 6 9 12 = 1, 2, 3, 4, 6, 12 1 2 3 18 = 1, 2, 3, 6, 9, 18 GCF = 2 x 3 = 6 GCF = 6 1 Multiples are products of a number when it is multiplied by a set of counting numbers Examples: The multiples of 7 are as follows: The multiples of 20 are as follows: 7, 14, 21, 28, 35, and others. 20, 40, 60, 80, 100 and others. 7x1=7 20 x 1 = 20 7 x 2 = 14 20 x 2 = 40 7 x 3 = 21 20 x 3 = 60 7 x 4 = 28 20 x 4 = 80 7 x 5 = 35 20 x 5 = 100 *Least Common Multiple Least Common Multiple (LCM) of two or more numbers is the least nonzero whole number which is a multiple of each of the numbers in a set. Decomposition/Continuous Division Listing Method LCM of 4, 8, 10 = ? LCM of 4, 8, 10 = ? 2 4 8 10 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 2 2 4 5 8 = 8, 16, 24, 32, 40, 48, 56, 64 2 1 2 5 10 = 10, 20, 30, 40, 50, 60, 70, 80 5 1 1 5 1 1 1 LCM = 2 x 2 x 2 x 5 = 40 LCM = 40 III. Prime and Composite Prime Numbers are numbers with two factors only, 1 and itself. Examples: 11 = 1 x 11 29 = 1 x 29 37 = 1 x 37 Composite Numbers are number with 3 or more factors. Examples: 4=1x4 =2x2 9=1x9 =3x3 15 = 1 x 15 =3x5 There are 25 prime numbers less than 100. These are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97. 0 and 1 are neither prime nor composite numbers. 2 is the only even number that is prime. 2 Practice Exercises 1. True or False ……………………….. (a) All numbers divisible by 2 are even numbers. ……………………….. (b) All odd numbers are prime numbers. ……………………….. (c) One is a factor of any whole number. ……………………….. (d) Multiples and products are the same. ……………………….. (e) Zero is a multiple of any number. 2. Fill in the blanks. (a) The sum of two odd numbers is ……………………….. . (b) The sum of an odd and an even number is always ……………………….. . 3. Differentiate a prime number from a composite number by accomplishing the table below. The first one is done for you. Counting Number List of Factors Number of Factors Prime Number 7 1, 7 2 ✓ Composite Number 19 27 49 56 78 4. List all the factors of the given set of numbers then encircle the GCF. (a) 8 = 16 = 20 = (b) 10 = 25 = 30 = 5. List the first 5 multiples of the given set of numbers and encircle the LCM. (a) 12 = 36 = (b) 9 = 15 = 45 = 3 20 Name: _______________________Class: 6________ CN:_______ Parents’ Signature: ______ Number Theory Math Worksheet #10 Term 1 1. True of False ……………………….. (a) The sum of two odd numbers is always odd. ……………………….. (b) Odd x even = even ……………………….. (c) All even numbers except 2 are composite numbers. ……………………….. (d) 1 is neither prime nor composite. [4] 2. Read and answer each statement. (a) What are the 5 odd numbers right before 100? …………………………………………………….…………………………… (b) Enumerate all the even numbers between 55 and 70. …………………………………………………….…………………………… (c) Write the first three composite numbers after 61. …………………………………………………….…………………………… (d) List down the factors of the following numbers. 44 = …………………………………………………….…………………………………………………….……………………………………………………. 67 = …………………………………………………….…………………………………………………….……………………………………………………. (e) List down the first 5 multiples of the given numbers. 16 = …………………………………………………….…………………………………………………….……………………………………………………. 21 = …………………………………………………….…………………………………………………….……………………………………………………. [7] 3. Use any method to solve for the GCF and LCM of each set of numbers. Write your solution (1pt/item) GCF LCM (a) 16, 24, 32 ……………………………….. ……………………………….. (b) 14, 21, 28 ……………………………….. ……………………………….. (c) 32, 40, 48 ……………………………….. ……………………………….. [9] 4