- \n
- Factors<\/a><\/li>\n
- Factor Tree Method<\/a><\/li>\n
- Properties of multiples<\/a><\/li>\n<\/ul>\n
Factor – Definition<\/h3>\n
Factors are defined as the numbers that are multiplied to give the product. For Example, Factors of 18 are 1, 2 3, 6, 9, 18. All these divide the number 18 exactly.<\/p>\n
Chart of Properties of Factors<\/h3>\n
Here is the Factors Properties Chart the lists the major properties. You can employ them while solving related problems and arrive at solutions easily.<\/p>\n
![\"Chart](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/06\/Chart-of-Properties-of-Factors.png\")
<\/p>\nProperties of Factors<\/h3>\n
Follow the properties given below to know how to find the factors of the multiples.<\/p>\n
Property 1.<\/strong>
\n1 is a factor of every number.
\nExample:<\/strong>
\nMultiply 1 with any number you get the same number.
\n1 \u00d7 31 = 31
\n1 \u00d7 534 = 534
\n1 \u00d7 76 = 76
\n1 \u00d7 467 = 467
\nProperty 2.<\/strong>
\nEvery number is a factor of itself.
\nExample:<\/strong> Multiply any number with 1 you get the original number.
\n15 \u00d7 1 = 15
\n5464 \u00d7 1 = 5464
\n530 \u00d7 1 = 530
\n66468 \u00d7 1 = 66468
\nProperty 3.<\/strong>
\nEvery factor of a number is an exact divisor of that number.
\nExample:<\/strong>
\nFactors of 10 are 1, 2, 5, 10.
\nHere each factor is exactly divisible by 10.
\nProperty 4.<\/strong>
\nEvery factor of a number is less than or equal to the number.
\nExample:<\/strong>
\n6 = 2 \u00d7 3
\nHere 2 and 3 are the factors that are less than 6.
\nProperty 5.<\/strong>
\nFactors of a given number are finite.
\nProperty 6.<\/strong>
\nEvery multiple of a number is greater than or equal to that number.
\nExample:<\/strong>
\nMultiple of 2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20.
\nProperty 7.<\/strong>
\nEvery number is multiple in itself.
\nProperty 8.<\/strong>
\nThe number of multiples of a given number is infinite.<\/p>\nExamples on Finding the Factors using Properties<\/h3>\n
Example 1.<\/strong>
\nFind the factors of 8 using the factor tree method.
\nSolution:
\n![\"Properties](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/06\/Properties-of-factors-img_1-300x239.jpg\")
<\/strong>
\nFactor tree of 8 is the list of prime numbers when multiplied results in the original number.
\nIf we write into multiples it would be 4 \u00d7 2.
\nOn splitting 4 further and writing it as multiples of number it would be 2 \u00d7 2.
\nAltogether expressing the number in terms of prime factors would be 2 \u00d7 2 \u00d7 2.<\/p>\nExample 2.<\/strong>
\nFind the factors of 72 using the factor tree method.
\nSolution:
\n![\"properties](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/06\/properties-of-factors-img_2-221x300.jpg\")
<\/strong>
\n72 = 2 \u00d7 36
\n9 = 3 \u00d7 3
\nSplit 72 into two pairs 2 \u00d7 36
\nNow split 36 we get 36 = 2 \u00d7 18
\nNow split the factors of 18 into two 18 = 2 \u00d7 9.
\nOn splitting 9 we get 3 \u00d7 3.
\nAltogether expressing the number in terms of prime factors 2 \u00d7 2 \u00d7 2 \u00d7 3 \u00d7 3.<\/p>\nExample 3.<\/strong>
\nWhat are the factors of 18?
\nSolution:<\/strong>
\nThe factors of 18 are as follows
\n1 \u00d7 18
\n2 \u00d7 9
\n3 \u00d7 6
\n6 \u00d7 3
\n9 \u00d7 2
\n18 \u00d7 1
\nThus the factors of 18 are 1, 2, 3, 6, 9, and 18.<\/p>\nExample 4.<\/strong>
\nWhat are the prime factors of 25?
\nSolution:<\/strong>
\nPrime factors of a number are the set of prime numbers which when multiplied by together give the actual number.
\nWe have to multiply directly with the prime number to find the factors of 25.
\n25 = 5 \u00d7 5
\nThus the prime factors of 25 are 5.<\/p>\nExample 5.<\/strong>
\nWhat are the factors of 30?
\nSolution:<\/strong>
\nThe factors of 30 are as follows
\n30 = 1 \u00d7 30
\n30 = 2 \u00d7 15
\n30 = 3 \u00d7 10
\n30 = 5 \u00d7 6
\n30 = 6 \u00d7 5
\n30 = 10 \u00d7 3
\n30 = 15 \u00d7 2
\n30 = 30 \u00d7 1
\nThus the factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.<\/p>\nFAQs on Properties of Factors<\/h3>\n
1. What are the properties of factors?<\/strong><\/p>\n
1. Smallest Multiple is the Number itself.
\n2. There can be an infinite number of multiples.
\n3. Multiples are greater than or equal to the given number.<\/p>\n2. What is a factor?<\/strong><\/p>\n
A factor is a number or an algebraic expression that divides another number or expression evenly with no remainder.<\/p>\n
3. How many types of factors are there?<\/strong><\/p>\n
Factors are classified into two types.
\n1. Prime factors
\n2. Composite factors<\/p>\n","protected":false},"excerpt":{"rendered":"A factor is one of two or more numbers that divides a given number without a remainder. Here we learn the different properties of factors to solve the problems. Know how to find the factors of different numbers from here. There are two methods to find the factors of the numbers. They are the division … Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":117540,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/06\/Properties-of-Factors.png","_links":{"self":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/117391"}],"collection":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/comments?post=117391"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/117391\/revisions"}],"predecessor-version":[{"id":135453,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/117391\/revisions\/135453"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media\/117540"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=117391"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=117391"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=117391"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
- Factor Tree Method<\/a><\/li>\n