{"id":18499,"date":"2019-09-01T15:01:48","date_gmt":"2019-09-01T20:01:48","guid":{"rendered":"http:\/\/www.kaptest.com\/blog\/prep\/?p=18499"},"modified":"2020-09-11T20:41:02","modified_gmt":"2020-09-11T20:41:02","slug":"gre-quantitative-prime-factorization","status":"publish","type":"post","link":"https:\/\/wpapp.kaptest.com\/study\/gre\/gre-quantitative-prime-factorization\/","title":{"rendered":"GRE Quantitative: Prime Factorization"},"content":{"rendered":"

As any Kaplan GRE Expert will tell you, the\u00a0Quantitative section<\/a>\u00a0is a test of concepts, not calculations. It\u2019s also a psychological test, designed to intimidate the rookie test-taker with big, scary-looking numbers.
\nFortunately, there\u2019s always a method to the GRE\u2019s math madness and, consequently, a way of making those intimidating numbers easier to understand. That\u2019s where the factor tree comes in\u2014one of the most powerful weapons to add to your\u00a0GRE math<\/a>\u00a0arsenal.<\/p>\n

Factor tree basics<\/b><\/h4>\n

You may remember (fondly or not) making a factor tree in grammar school. Factor trees allow you to break a large number down into smaller, more manageable parts.
\nFirst, we should review the basics of how to find prime factors. We begin by using a garden variety factor tree whose fruit is composed of the essence of any positive, non-prime integer.
\nSuppose we want to find the prime factors of 60:
\n\"image\"<\/a>
\nWe can start with any two factors of 60 that are each less than 60, but together multiply to 60. Here, we use 2 and 30. Every time you hit a prime number, circle it, because that \u201cbranch\u201d of the factor tree has reached its end. In this example, 2 is prime, so we circle it.
\nThen, we can break down 30 in the same way: We use 3 and 10, circling 3, since it\u2019s prime. We then break 10 into 2 and 5, each of which is prime and gets circled as well.
\nThis tells us a few things about the number 60. First, it tells us that its prime factors are 2, 3, and 5. Perhaps more importantly, it tells us that 60 can be expressed by multiplying all those numbers we circled a moment ago: 2 x 2 x 3 x 5.<\/p>\n

Know your prime numbers<\/b><\/h4>\n

Prime numbers are the building blocks of any positive non-prime integer. In other words, any positive non-prime integer can be expressed as a bunch of prime numbers multiplied together.
\nIt would certainly behoove any aspiring\u00a0GRE<\/a>\u00a0champion to therefore memorize at least the first handful of prime numbers: 2, 3, 5, 7, 11, 13. You\u2019ll notice that 2 is the smallest and the only even prime number. Remember, not all odd numbers after 2 are prime (you\u2019ll notice that 9 is not prime because it is divisible by 3, for instance)\u2014but after 2, all prime numbers are odd.<\/p>\n

Making GRE math manageable<\/b><\/h4>\n

Finding prime factors can save you time and effort on the Quantitative section of the GRE if you know how to apply the concept. Whenever you feel like the GRE is trying to make you multiply or divide very large numbers\u2014let\u2019s use the very technical term \u201cBUNs,\u201d or Big Ugly Numbers\u2014there\u2019s a good chance that the shortcut involves prime factorization.
\nImagine that the GRE gives you the following equation and asks you to solve for the value of\u00a0b<\/i>:
\n\"image<\/a>
\nIt would be time-consuming and inefficient on Test Day to determine what 105 x 105 x 105 is equal to, then find the actual value of 21 x 25 x 45, and then divide one BUN by another BUN.
\nThe Kaplan-trained student thinks: \u201cThe GRE could\u2019ve given me any numbers in the world, so there\u00a0has<\/i>\u00a0to be some reason that they chose these.\u201d In fact,\u00a0this problem lends itself quite nicely to prime factorization, in which the math itself is relatively innocuous.<\/p>\n

Prime factors are your friend<\/b><\/h4>\n

To solve the problem above, let\u2019s start with the denominator. Using factor trees, we find out 21 = 3 x 7, 25 = 5 x 5, and 45 = 3 x 3 x 5.
\nNow let\u2019s move to the numerator. The problem says 105\u00b3\u2014so let\u2019s just start with 105. Just by looking at 105, we know it\u2019s divisible by 5, but 105 is 5 times what? Well, 5 x 20 would equal 100, in which case we\u2019d need one more 5. So, 105 = 5 x 21, and 21 breaks down into 3 x 7 as we saw a moment ago. Therefore, 105 = 3 x 5 x 7. We have 105\u00b3, however. So, we must rewrite 3 x 5 x 7 a total of 3 times for the numerator. Now we have:
\n\"image<\/a>
\nThis becomes an exercise in what mathematicians call\u2014to use even more technical terminology\u2014\u201dcrossing stuff out.\u201d Let\u2019s cross off\u00a0as many numbers on the top and bottom as we can, and see what is left standing. Cross out all of the 3\u2019s, all of the 5\u2019s, and just one 7 from the top and bottom\u2014and\u00a0voila<\/i>: we are left simply with 7 x 7, or 49.
\nIt involved some writing, but the math itself didn\u2019t hurt too much now, did it?
\nWant to try out your factor tree skills? Sign up for a\u00a0<\/i>free GRE practice test<\/i><\/a>\u00a0and start building the confidence you need to boost your Quantitative score.<\/i><\/p>\n

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As any Kaplan GRE Expert will tell you, the\u00a0Quantitative section\u00a0is a test of concepts, not calculations. It\u2019s also a psychological test, designed to intimidate the rookie test-taker with big, scary-looking numbers. Fortunately, there\u2019s always a method to the GRE\u2019s math madness and, consequently, a way of making those intimidating numbers easier to understand. That\u2019s where […]<\/p>\n","protected":false},"author":1,"featured_media":27056,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[68],"tags":[375,316,379],"_links":{"self":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/18499"}],"collection":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/comments?post=18499"}],"version-history":[{"count":2,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/18499\/revisions"}],"predecessor-version":[{"id":34549,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/18499\/revisions\/34549"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/media\/27056"}],"wp:attachment":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/media?parent=18499"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/categories?post=18499"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/tags?post=18499"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}