factors,)mul-ples)and) divisibility
TRANSCRIPT
Introduction:�Factors multiples and divisibilit3 deal with dividing and multiplying positive integers {1,2,3,4, . . .}. In this chapter you will work with such concepts as Greatest Common Factor (GCF) and Least Common Multiple (LCM). You will use the factors and multiples of a number to help you solve a variet3 of SAT Problems.
Factors:�A factor of a whole number divides the number, with no remainder. Example:
Is 6 a factor of 50? Because 6 divides into 50 eight times with remainder 2, 6 is not a factor of 50. Example:
Is 7 a factor of 63? Because 7 divides into 63 nine times without a remainder, 7 is a factor of 63.
PRIMES AND COMPOSITES �A prime number is a positive integer that has exactly t6o factors, 1 and itself A composite is a positive integer that has more than t6o factors Example: Is 20 a prime or composite number? The factors of 20 are {1,2,4,5,10,20}. Therefore, 20 is a composite number. Example: Is 17 a prime or composite number? The factors of 17 are {1,17}. Therefore, 17 is a prime number.
GREATEST COMMON FACTOR (GCF) �The GREATEST COMMON FACTOR (GCF) of t6o numbers is the largest factor the t6o numbers have in common. Example: What is the GCF of 16 and 36? The factors of 16 are {1,2,4,8,16}, and the factors of 36 are {1,2,3,4,6,9,12, 18,36}. Therefore, the GCF is 4.
MULTIPLES �The MULTIPLES of a given number are those numbers created by successive multiplication. The given number divides the multiple without a remainder. Example: List the first five multiples of 3 and the first five multiples of 6. The multiples of 3 are {3,6,9,12,15}, and the multiples of 6 are {6,12,18, 24,30}.
LEAST COMMON MULTIPLE (LCM) �The LEAST COMMON MULTIPLE (LCM) is the smallest multiple t6o numbers have in common. Example: What is the LCM of 3 and 6? Answer: 6 6 is the smallest multiple these numbers have in common.
Divisibility:�If you divide one number by another, the result is a whole number without a remainder. Example: 12 / 6 =2 No remainder, so 12 is divisible by 6.
What is the greatest number of 3s that can be multiplied together and still
have a result less than 250?��� A. 3
B. 4
C. 5
D. 6
E. 7
Which of the following must be true about the sum of all the prime numbers
between 20 and 30? ������ A. It is a prime number.
B. It is an odd number.
C. It is a factor of 156.
D. It is a multiple of 5.
E. It is a factor of 10.
What is the greatest integer that evenly divides both 48 and 64? The largest integer that evenly divides both
48 and 64 is the GCF of the two numbers.
The factors of 48 are
{1,2,3,4,6,8,12,16,24,48}.
The factors of 64 are {1,2,4,8,16,32,64}.
The GCF is 16.
Answer: 16