{"id":92,"date":"2014-01-28t09:00:08","date_gmt":"2014-01-28t09:00:08","guid":{"rendered":"\/\/www.catharsisit.com\/act\/?p=92"},"modified":"2015-04-15t00:02:20","modified_gmt":"2015-04-15t00:02:20","slug":"act-number-properties-basics-factors-multiples-and-divisibility","status":"publish","type":"post","link":"\/\/www.catharsisit.com\/hs\/act\/act-number-properties-basics-factors-multiples-and-divisibility\/","title":{"rendered":"act number properties basics: factors, multiples, and divisibility"},"content":{"rendered":"

act math basics<\/h2>\n

learning the basics of number properties is crucial for success on the act math test<\/a>. here, you’ll learn some basic terminology to help you on the test.<\/p>\n

a factor<\/b>, or divisor, of a number is a positive integer that evenly divides into that number. for example, 4 is a factor of 12 because 12\/4 is an integer, 3. all integers have 1 and themselves as factors. for example there are six factors for the number 12: 1, 2, 3, 4, 6, 12.<\/p>\n

the gcf, or greatest common factor<\/b>, is the biggest factor that two numbers have in common. think of gcf questions as: what is the biggest number that divides evenly into both?<\/p>\n

a prime number<\/b> is a special kind of integer that has exactly two factors: itself and 1.<\/p>\n

remember that 1 is not prime, because it only has one factor, itself. 2 is a special number because it is the smallest prime number and the only even prime number. the first few prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.<\/p>\n

a multiple<\/b> is a number that is evenly divisible by another integer. for example, 6 is a multiple of 3. 10 is a multiple of 5. the multiple is always larger<\/i> than the other integer. the other integer would be considered a factor of the multiple. every number is a multiple of itself.<\/p>\n

for example, for the number 12, possible multiples are 12, 24, 36, 48, 60, etc. the lcm, or lowest common multiple<\/b>, is the smallest number for which both given numbers are factors.
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practice question<\/h2>\n

what is the lcm of 12 and 9?<\/i><\/p>\n

9 = 3 x 3, and 12 = 3 x 4, so the lcm must be 3 x 3 x 4 = 36. by saying that the lcm of 12 and 9 is 36, you are saying that 36 is the smallest number that both 12 and 9 will divide into evenly. notice how the lcm is not necessarily just the product of the two integers.
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the act math rules of divisibility<\/h2>\n

in addition to factors and multiples, it helps to know some basic divisibility rules \u2013 a great shortcut on certain long division problems!<\/p>\n