{"id":1037,"date":"2013-04-22t09:00:37","date_gmt":"2013-04-22t09:00:37","guid":{"rendered":"\/\/www.catharsisit.com\/sat\/?p=1037"},"modified":"2018-10-20t14:18:38","modified_gmt":"2018-10-20t21:18:38","slug":"number-properties-and-factor-trees-on-the-sat","status":"publish","type":"post","link":"\/\/www.catharsisit.com\/hs\/sat\/number-properties-and-factor-trees-on-the-sat\/","title":{"rendered":"number properties and factor trees on the sat"},"content":{"rendered":"

sat math loves number properties<\/a> <\/span>almost as much as it loves triangles<\/a>. of course, that\u2019s actually a wide range of topics. number properties describe how integers can be broken down, combined, or worked with in different ways; exponent patterns, odds and evens, positives and negatives, and divisibility all fall under the number property umbrella, as do others.<\/p>\n

getting these question right on your sat comes down to a few things. the most important is simply knowing rules (e.g. negative times negative is positive). beyond that, you also have to be capable of finding patterns in numbers. doing a little bit of experimenting and looking for rhyme or reason pays off. you also have to see numbers inside<\/i> numbers.<\/p>\n

that is, if you see a 21, you should immediately recognize that\u2019s 7 times 3 and be ready to work with that fact. questions that ask about factors and multiples are perfect examples of how the sat assesses that skill.<\/p>\n

 <\/p>\n

splitting integers up<\/h2>\n

you\u2019re probably already pretty familiar with factor trees, so i\u2019m not going to bore you with how to make one. but just in case you\u2019re a little fuzzy on what it looks like:<\/p>\n

\"npaftfts_img1\"<\/a><\/p>\n

\u2026such a comfortable, familiar shape. i learned how to draw a christmas tree like that when i was in kindergarten and i\u2019ve been doing it ever since. (clearly, i am quite the artist.<\/a>)<\/p>\n

by the way, you should remember that those factors hanging off of the very bottom of our tree are all prime numbers<\/a>.<\/p>\n

 <\/p>\n

least common multiple<\/h2>\n

though the sat rarely uses the terms, you should definitely be comfortable finding both least common multiples and the greatest common factors before you take the test.<\/p>\n

the lcm is the smallest number that includes all <\/i>of the prime factors of both<\/i> numbers.<\/p>\n

sometimes that means just multiplying all of the numbers together if the two numbers don\u2019t share any common factors.<\/p>\n

\"npaftfts_img2\"<\/a><\/p>\n

sometimes it means taking just as many as you need.<\/p>\n

\"npaftfts_img3\"<\/a><\/p>\n

since 4 gave us 2 as a factor twice, we don\u2019t need to use the 2 from the factors of 6.<\/p>\n

 <\/p>\n

greatest common factor<\/h2>\n

the greatest common factor is pretty similar. get the prime factors of both numbers, then find what\u2019s in common. sometimes there\u2019s nothing shared, like with 9 and 4 above, which means the gcf is 1 (both are divisible by 1, after all). sometimes there\u2019s only one factor in common, like with 6 and 4 above. in that case, the gcf is 2, since that\u2019s the only factor they share.<\/p>\n

but sometimes, you need to multiply together shared factors.<\/p>\n

\"npaftfts_img4\"<\/a><\/p>\n

if you want to be extra careful, you can always divide both number by that gcf you got.<\/p>\n

 <\/p>\n

all of the factors<\/h2>\n

sometimes you\u2019ll need to find all<\/i> of the factors of a specific number. that means making a factor tree, then combining those prime factors in every possible way.<\/p>\n

lets use that factor tree for the number 84.<\/p>\n

\"npaftfts_img5\"<\/a><\/p>\n

those prime factors are a start. also, remember that every list of factors should start with the number 1, since it\u2019s a factor of every integer.<\/p>\n

so our list so far is 1, 2, 3, and 7.<\/p>\n

now, let\u2019s combine them. let\u2019s start with the 2 furthest on the right, and combine it with every other prime factor.<\/p>\n

\"2*2=4\"<\/p>\n

\"2*3=6\"<\/p>\n

\"2*7=14\"<\/p>\n

so we can add 4, 6, and 14 to the list.<\/p>\n

now let\u2019s combine that 2 with pairs<\/i> of the other prime factors.<\/p>\n

\"2*2*3=12\"<\/p>\n

\"2*2*7=28\"<\/p>\n

\"2*3*7=42\"<\/p>\n

add 12, 28, and 42 to the list….<\/p>\n

then we\u2019re done using the first 2, so cross it off.<\/p>\n

\"npaftfts_img6\"<\/a><\/p>\n

keep going with the next factor. using the other 2 is pointless though\u2026<\/p>\n

\"2*3=6\"<\/p>\n

\"2*7=14\"<\/p>\n

\"2*3*7=42\"<\/p>\n

we\u2019ve seen those before, so we\u2019ll move on.<\/p>\n

\"npaftfts_img7\"<\/a><\/p>\n

now we can combine 3 and 7.<\/p>\n

\"3*7=21\"<\/p>\n

so we add 21 to the list.<\/p>\n

after that, the only piece left is the largest factor of all: 84.<\/p>\n

our list is now 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.<\/p>\n

if you have to get all the factors of a number, do it systematically.<\/i> don\u2019t just start listing whatever you can think of\u2014you\u2019re bound to miss one that way. and never forget 1 and the number itself.<\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

sat math loves number properties almost as much as it loves triangles. of course, that\u2019s actually a wide range of topics. number properties describe how integers can be broken down, combined, or worked with in different ways; exponent patterns, odds and evens, positives and negatives, and divisibility all fall under the number property umbrella, as […]<\/p>\n","protected":false},"author":42,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[91],"tags":[58,81],"ppma_author":[24883],"acf":[],"yoast_head":"\nnumber properties and factor trees on the sat - magoosh blog | high school<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"\/\/www.catharsisit.com\/hs\/sat\/number-properties-and-factor-trees-on-the-sat\/\" \/>\n<meta property=\"og:locale\" content=\"en_us\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"number properties and factor trees on the sat\" \/>\n<meta property=\"og:description\" content=\"sat math loves number properties almost as much as it loves triangles. of course, that\u2019s actually a wide range of topics. number properties describe how integers can be broken down, combined, or worked with in different ways; exponent patterns, odds and evens, positives and negatives, and divisibility all fall under the number property umbrella, as […]\" \/>\n<meta property=\"og:url\" content=\"\/\/www.catharsisit.com\/hs\/sat\/number-properties-and-factor-trees-on-the-sat\/\" \/>\n<meta property=\"og:site_name\" content=\"magoosh blog | high school\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/magooshsat\/\" \/>\n<meta property=\"article:published_time\" content=\"2013-04-22t09:00:37+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2018-10-20t21:18:38+00:00\" \/>\n<meta property=\"og:image\" content=\"\/\/www.catharsisit.com\/sat\/files\/2013\/04\/npaftfts_img1.png\" \/>\n<meta name=\"author\" content=\"lucas fink\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@magooshsat_act\" \/>\n<meta name=\"twitter:site\" content=\"@magooshsat_act\" \/>\n<meta name=\"twitter:label1\" content=\"written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"lucas fink\" \/>\n\t<meta name=\"twitter:label2\" content=\"est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"article\",\"@id\":\"\/\/www.catharsisit.com\/hs\/sat\/number-properties-and-factor-trees-on-the-sat\/#article\",\"ispartof\":{\"@id\":\"\/\/www.catharsisit.com\/hs\/sat\/number-properties-and-factor-trees-on-the-sat\/\"},\"author\":{\"name\":\"lucas fink\",\"@id\":\"\/\/www.catharsisit.com\/hs\/#\/schema\/person\/c06e6a007d0b81117c00610ed88b6c7d\"},\"headline\":\"number properties and factor trees on the sat\",\"datepublished\":\"2013-04-22t09:00:37+00:00\",\"datemodified\":\"2018-10-20t21:18:38+00:00\",\"mainentityofpage\":{\"@id\":\"\/\/www.catharsisit.com\/hs\/sat\/number-properties-and-factor-trees-on-the-sat\/\"},\"wordcount\":696,\"commentcount\":0,\"publisher\":{\"@id\":\"\/\/www.catharsisit.com\/hs\/#organization\"},\"keywords\":[\"sat integer properties\",\"sat math section\"],\"articlesection\":[\"sat\"],\"inlanguage\":\"en-us\",\"potentialaction\":[{\"@type\":\"commentaction\",\"name\":\"comment\",\"target\":[\"\/\/www.catharsisit.com\/hs\/sat\/number-properties-and-factor-trees-on-the-sat\/#respond\"]}]},{\"@type\":\"webpage\",\"@id\":\"\/\/www.catharsisit.com\/hs\/sat\/number-properties-and-factor-trees-on-the-sat\/\",\"url\":\"\/\/www.catharsisit.com\/hs\/sat\/number-properties-and-factor-trees-on-the-sat\/\",\"name\":\"number properties and factor trees on the sat - 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