FACTORS AND MULTIPLES FACTORS 12. Oral. The factors of a number are the whole numbers which multiplied together produce the number. 2, 3, and 5 are the factors of 30. Any exact divisor of a number is a factor of it. A prime number has no factors except itself and 1; as 5, 17. A composite number has other factors than itself and 1; as 6. Factoring is the process of separating a number into its factors. 1. What is a prime factor? An even number? An odd number? 2. Name all of the prime numbers between 1 and 100. 3. Give the prime factors of: 14, 15, 20, 21, 28, 30, 27, 18, 32, 40, 45, 36, 42, 48, 55, 60, 66, 70, 72, 75, 80, 84, 90, 100. A number is divisible: By 2, if it ends in 2, 4, 6, 8, or 0; as 24, 70. By 5, if it ends in 0, or 5; as 25, 40. By 3, if the sum of its digits is divisible by 3; as 72, 132. 4. Give six numbers greater than 300 that are divisible by 2; by 3; by 5. 13. Written. Find the prime factors of 420. The prime factors of 420 are 2, 2, 5, 3, and 7. 2 × 2 × 5 × 3 x 7 420. = If any number is not divisible by 2, 3, or 5, try in order the prime numbers 7, 11, 13, 17, etc., as divisors until you obtain a quotient no larger than the divisor used. If none of these divisors divides the number exactly, it is a prime number. A common factor of two or more numbers is a factor that is contained in each of them. 7 is a common factor of 21 and 35. The greatest common factor (G. C. F.) of two or more numbers is the greatest factor contained in each of them. 12 is the greatest common factor of 24, 36, and 48. Numbers that have no common factors are said to be prime to each other. 21 and 32 are prime to each other. Name the G. C. F. in each of the following sets of numbers: 1. 20, 40 4. 12, 18, 24 7. 24, 40, 48 10. 16, 32, 40, 48 11. 20, 40, 50, 60 12. 30, 60, 90, 120 15. Written. What is the G. C. F. of 42, 63, and 105? Find the G. C. F. 1. 33, 66, 121 2. 36, 72, 144 3. 48, 96, 120 4. 63, 90, 117 5. 39, 78, 117 Separate the numbers into their prime factors. The factors, 3 and 7, are common to all of the numbers Their product, 3 × 7, or 21, is the G. C. F. of: 6. 64, 128, 320 7. 70, 105, 280 8. 64, 160, 192 9. 84, 140, 168 10. 99, 165, 198 11. 72, 180, 252 A multiple of a number is another number that exactly contains it. 12, 18, and 42 are multiples of 6. A common multiple of two or more numbers is a number that exactly contains each of them. 84 is a common multiple of 2 and 7. The least common multiple (L. C. M.) of two or more numbers is the smallest number that exactly contains each of them. 14 is the L. C. M. of 2 and 7. take the product of all the different prime factors, using each the greatest number of times it occurs in any one number. Rejecting equal factors from both dividend and divisor in division is called cancelation. 28. At P45 per 100 liters, what will 25,300 liters of alcohol cost? 29. I paid P 2025 for 30 lots of 270 sq. m each. What did I pay per sq. m? 30. At P1.44 per dozen, how many loaves of bread will P18.72 purchase? A fraction is one or more of the equal parts of a unit. The numerator and denominator are the terms of the fraction. 1. What does the denominator show? The numerator? ૐ, 31, 5, 7, 88, 12 are mixed numbers. 2. Define proper fraction; improper fraction; mixed number. REDUCTION OF FRACTIONS TO HIGHER OR LOWER TERMS 20. Oral. Multiplying or dividing both terms of a fraction by the same number does not change its value. A fraction is in its lowest terms when its numerator and denominator are prime to each other. To reduce a fraction to lowest terms, cancel all the factors common to both of its terms. |