{"id":11973,"date":"2018-01-25T05:09:10","date_gmt":"2018-01-25T13:09:10","guid":{"rendered":"https:\/\/www.rocketmath.com\/?p=11973"},"modified":"2018-07-26T15:53:45","modified_gmt":"2018-07-26T22:53:45","slug":"foolproof-method-for-finding-factors","status":"publish","type":"post","link":"https:\/\/www.rocketmath.com\/stagingserver\/foolproof-method-for-finding-factors\/","title":{"rendered":"Foolproof method for finding factors"},"content":{"rendered":"

Knowing when you’ve found ALL the factors is the hard part.<\/strong><\/p>\n

Students have to learn how to find the factors of a number because several tasks in working with fractions require students to find the factors of numbers. Thinking of some <\/strong>of the factors of a number is not hard. What is hard is knowing when you have thought of ALL the factors. Here is a foolproof, systematic method I recommend: starting from 1 and working your way up the numbers. This is what student practice in the Rocket Math Factors program<\/a><\/span><\/span>.<\/p>\n

https:\/\/youtu.be\/fDYMRfxtGIc<\/a><\/p>\n

I have a white board type video lesson that explains this in 6 minutes.\u00a0https:\/\/youtu.be\/fDYMRfxtGIc<\/p>\n

Bookmark this link so you can show it to your students.<\/p>\n

How to find all the factors of numbers<\/strong>
\nAlways begin with 1 and the number itself-those are the first two factors. You write 1 x the number. \u00a0Then go on to 2. Write that under the 1. If the number you are finding factors for is an even number then 2 will be a factor. Think to yourself \u201c2 times what equals the number we are factoring?\u201d The answer will be the other factor.
\nHowever, if the number you are finding factors for is an odd number, then 2 will not be a factor and so you cross it out and go on to 3. Think to yourself \u201c3 times what equals the number we are factoring?\u201d There\u2019s no easy rule for 3s like there is for 2s. But if you know the multiplication facts you will know if there is something. Then you go on to four\u2014and so on.<\/p>\n

The numbers on the left start at 1 and go up in value. \u00a0The numbers on the right go down in value. \u00a0You know you are done when you come to a number on the left that you already have on the right. \u00a0Let\u2019s try an example.<\/p>\n

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

Let\u2019s find the factors of 18.<\/strong>\u00a0 (To the left you see a part of a page from the Rocket Math factoring program.)<\/em>
\nWe start with the first two factors, 1 and 18. We know that one times any number equals itself. We write those down.
\nNext we go to 2. 18 is an even number, so we know that 2 is a factor. We say to ourselves, \u201c2 times what number equals 18?\u201d The answer is 9. Two\u00a0times 9 is 18, so 2 and 9 are factors of 18.
\nNext we go to 3. We say to ourselves, \u201c3 times what number equals 18?\u201d The answer is 6. Three\u00a0times 6 is 18, so 3 and 6 are factors of 18.
\nNext we go to 4. We say to ourselves, \u201c4 times what number equals 18?\u201d There isn\u2019t a number. We know that 4 times 4 is 16 and 4 times 5 is 20, so we have skipped over 18. We cross out the 4 because it is not a factor of 18.
\nNext we go to 5. We might say to ourselves, \u201c5 times what number equals 18?\u201d But we know that 5 is not a factor of 18 because 18 does not end in 5 or 0 and only numbers that end in 5 and 0 have 5 as a factor. So we cross out the five.
\nWe would next go to 6, but we don\u2019t have to. If we look up here on the right side we see that 6 is already identified as a factor. So we have identified all the factors there are for 18. Any more factors that are higher we have already found. So we are done.<\/p>\n

Now let\u2019s do another number.\u00a0 Let\u2019s find the factors of 48.\u00a0<\/strong><\/p>\n

We start with the first two factors, 1 and 48.\u00a0 We know that one times any number equals itself.<\/p>\n

Next we go to 2.\u00a0 48 is an even number, so we know that 2 is a factor.\u00a0 We say to ourselves, \u201c2 times what number equals 48?\u201d\u00a0 We might have to divide 2 into 48 to find the answer is 24.\u00a0 But yes 2 and 24 are factors of 48.<\/p>\n

Next we go to 3.\u00a0 We say to ourselves, \u201c3 times what number equals 48?\u201d\u00a0\u00a0 The answer is 16.\u00a0 We might have to divide 3 into 48 to find the answer is 16.\u00a0 But yes 3 and 16 are factors of 48.<\/p>\n

Next we go to 4.\u00a0 We say to ourselves, \u201c4 times what number equals 48?\u201d\u00a0 If we know our 12s facts we know that 4 times 12 is 48.\u00a0 So 4 and 12 are factors of 48.<\/p>\n

Next we go to 5.\u00a0 We might say to ourselves, \u201c5 times what number equals 48?\u201d\u00a0\u00a0 But we know that 5 is not a factor of 48 because 48 does not end in 5 or 0 and only numbers that end in 5 and 0 have 5 as a factor. So we cross out the five.<\/p>\n

Next we go to 6. We say to ourselves, \u201c6 times what number equals 48?\u201d\u00a0 If we know our multiplication facts we know that 6 times 8 is 48.\u00a0 So 6 and 8 are factors of 48.<\/p>\n

Next we go to 7.\u00a0\u00a0 We say to ourselves, \u201c7 times what number equals 48?\u201d\u00a0\u00a0 There isn\u2019t a number.\u00a0 We know that 7 times 6 is 42 and 7 times 7 is 49, so we have skipped over 48.\u00a0 We cross out the 7 because it is not a factor of 48.<\/p>\n

We would next go to 8, but we don\u2019t have to.\u00a0 If we look up here on the right side we see that 8 is already identified as a factor.\u00a0 So we have identified all the factors there are for 48.\u00a0 Any more factors that are higher we have already found.\u00a0 So we are done.<\/p>\n","protected":false},"excerpt":{"rendered":"

Knowing when you’ve found ALL the factors is the hard part. Students have to learn how to find the factors of a number because several tasks in working with fractions require students to find the factors of numbers. Thinking of some of the factors of a number is not hard. What is hard is knowing […]<\/p>\n","protected":false},"author":2,"featured_media":12008,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"pmpro_default_level":0},"categories":[41,42],"tags":[35,48,38],"_links":{"self":[{"href":"https:\/\/www.rocketmath.com\/stagingserver\/wp-json\/wp\/v2\/posts\/11973"}],"collection":[{"href":"https:\/\/www.rocketmath.com\/stagingserver\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.rocketmath.com\/stagingserver\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.rocketmath.com\/stagingserver\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.rocketmath.com\/stagingserver\/wp-json\/wp\/v2\/comments?post=11973"}],"version-history":[{"count":5,"href":"https:\/\/www.rocketmath.com\/stagingserver\/wp-json\/wp\/v2\/posts\/11973\/revisions"}],"predecessor-version":[{"id":35805,"href":"https:\/\/www.rocketmath.com\/stagingserver\/wp-json\/wp\/v2\/posts\/11973\/revisions\/35805"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.rocketmath.com\/stagingserver\/wp-json\/wp\/v2\/media\/12008"}],"wp:attachment":[{"href":"https:\/\/www.rocketmath.com\/stagingserver\/wp-json\/wp\/v2\/media?parent=11973"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.rocketmath.com\/stagingserver\/wp-json\/wp\/v2\/categories?post=11973"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.rocketmath.com\/stagingserver\/wp-json\/wp\/v2\/tags?post=11973"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}