{"id":92,"date":"2014-01-28T09:00:08","date_gmt":"2014-01-28T09:00:08","guid":{"rendered":"https:\/\/magoosh.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":"https:\/\/magoosh.com\/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