Factors and Multiples

March 25, 2018 | Author: RensieViqueFalculan | Category: Prime Number, Integer, Division (Mathematics), Elementary Mathematics, Abstract Algebra


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MATH 101 – Fundamentals of MathematicsRepublic of the Philippines BATANGAS STATE UNIVERSITY Jose P. Laurel Polytechnic College Malvar, Batangas College of Teacher Education Fundamentals of Mathematics FACTORS, MULTIPLES & INTEGERS The factors of integer n are the positive integers that divide n evenly without remainder. Ex. factors of 24: 1, 2, 3, 4, 6, 8, 12, and 24 The multiples of n are integers that n divide without any remainder. Ex. multiples of 7: 7, 14, 21, 28, 35 … Prime numbers – counting numbers that have exactly two distinct, positive divisors. There are 25 prime numbers from 1 to 100. Composite numbers – counting numbers greater than 1 that have positive factors other than 1 and itself. PRIME FACTORIZATION – expressing a number as a product of factors, each of which is a prime number.  Factor Tree  Continuous Division Find the prime factors of the following. 1. 1225 4. 3762 2. 980 5. 1584 3. 450 6. 7. GREATEST COMMON FACTOR (GCF) – refers to the largest common factor of two or more numbers. 8. Ex. Find the GCF of 45 and 60. 9. 10.Find the greater common factor of the following. 1. 441, 147 5. 120, 180, 150 2. 80, 200 6. 84, 294, 126 3. 225, 135 7. 1296, 864 4. 216, 144 8. 9. LEAST COMMON MULTIPLE (LCM) – refers to the smallest number that two or more numbers will divide without remainder. 10. Ex. Find the LCM of 18 and 20. 11. 12.Find the least common multiple of the following. 1. 60, 72 5. 36, 45, 30 2. 20, 36, 24 6. 44, 33, 36 3. 12, 14, 21 7. 18, 45, 20 4. 28, 21, 42 8. 9. Solve the following. 1. What is the difference between the largest prime number and smallest prime number between 50 and 90? 2. What is the smallest positive integer that has factors of 3, 4, 5, and 6? 3. A man has two trees he wishes to cut into logs of equal length. If the trees are 84 dm and 96 dm long, and are cut into the longest possible logs, what is the length of the log? 4. A man had 152g and 140g of peanuts which he wishes to put into boxes. Each box should hold same number of grams and largest number possible. How many grams can he put into each box? 5. How many integers between 1 and 150 are divisible by both 4 and 5? 10. 11. INTEGERS a+ (−a ) =0. 42. | | 7. 55. (−6)+(−10)=−16 34. 13.MATH 101 – Fundamentals of Mathematics 12.Additive Inverse – If a is an integer.Examples: 40. there exists the additive inverse or simply called the negative denoted by –a. Divisio n 47.Add the integers and keep the sign. Multip lication 45. ABSOLUTE VALUE It refers to the number of units a number is away the number line. Operat 21. 12. (−32 ) ÷ (−8 )=4 52. 23. such that 13. 5+3=8 33. (−9 ) (5 )=−45 50. 59. (−9)– (−5)=(−9)+5=−4 43. 15. 44. 25. Ex. 8. −2 ( 3 ) (−5 ) — 8(2) ( −816 ) 8 (−2 )−4 (3 )− 10 21 − −2 3 −8 12 − 10. 27. 58. and 46. 37. −2 8 5.Subtract the integers and take the sign of the integer with the largest absolute value. (3)(7)=21 57. −4 ( 5 ) — 2(−9) 9. 49. 100 ÷ (−10 )=−10 51. 7+(−4)=3 29. 17. Like Signs ion Additi on 22.Examples: 56. 60. 36. 30. 31. |-7|= 7 20.Examples: Subtra ction Unlike Signs 28. −4 −2 ( ) 11.If the signs are different. |7−(−11 )| 3. 26. 16. 54. It refers to the set of whole numbers and their opposites. 14. |−2−7| 2.Evaluate the following.Change the sign of the subtrahend and then proceed to addition. 48. 39. 1. . (−9)+ 4=−5 35.Examples: 53.If the signs of the factors or dividend/divisors are the same. 4 – (−6)=4+ 6=10 41. the product/quotient is positive.Examples: 24. the product/quotient is negative. 18. 32. OPERATIONS ON SIGNED NUMBERS 19. |– (−2 )−(−17)| 6. 38. |−8−9| 4. 24 2. 16.MATH 101 – Fundamentals of Mathematics 14. −24 6 5. there exist a multiplicative inverse or 1 simple called the reciprocal. such that a ( 1a )=1. Multiplicative Inverse – if a is an integer.Find the additive and multiplicative inverses of the following integers. 15. -16 3. −5 10 . 2 3 4. denoted by a . 1. 8. Rensie Vique F. Ms.6. Falculan 11. 10.Instructor . Prepared by: 9. 7.
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