{"id":265,"date":"2024-04-01T14:05:32","date_gmt":"2024-04-01T13:05:32","guid":{"rendered":"https:\/\/tutors4you.com\/?page_id=265"},"modified":"2024-04-01T14:05:33","modified_gmt":"2024-04-01T13:05:33","slug":"tutorial-on-integers","status":"publish","type":"page","link":"https:\/\/tutors4you.com\/index.php\/tutorial-on-integers\/","title":{"rendered":"Tutorial on Integers"},"content":{"rendered":"\n\n\t\t
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The numbers -3,-2,-1,0,1,2,3 are all\n integers. -1,-2, and -3 are negative integers. Similarly\n +1,+2,+3 are positive integers, however we write them as\n 1,2 ,3 leaving out the + sign. 0 is also an integer.<\/font><\/p>\n

Multiples
\n <\/u>If we multiply 5 by 3 the answer will be 15. We may\n write this as:<\/font><\/p>\n

5 x 3 = 15<\/font><\/p>\n

We say that 15 is a multiple of both 5 and\n 3;<\/font><\/p>\n

Factors
\n <\/u>12 can be divided by any of the following numbers:<\/font><\/p>\n

1,2,3,4,6 and 12 itself<\/font><\/p>\n

All these numbers are called factors of 12<\/font><\/p>\n

Prime Numbers<\/u>
\n A prime number has only two factors, these are 1 and the\n prime number itself. Examples of prime numbers are:<\/font><\/p>\n

3 its factors are 1,3
\n 5 its factors are 1,5
\n 7 its factors are 1,7
\n and so on<\/font><\/p>\n

Any integer greater than 1 is either a prime\n number or can be written as a product of prime numbers.\n For example:<\/font><\/p>\n

2: a prime number
\n 3: a prime number
\n 4= 2 x 2: 2 is a prime number
\n 5: a prime number
\n 6= 2 x 3: 2 and 3 are prime numbers
\n 7: a prime number
\n 8= 2 x 2 x 2: 2 is a prime number
\n 9= 3 x 3: 3 is a prime number
\n 10= 2 x 5: 2 and 5 are prime numbers
\n and so on<\/font><\/p>\n

Common Multiples
\n <\/u>8 is a common multiple of 2 and 4
\n 10 is a common multiple of 2 and 5
\n 12 is a common multiple of 2,3,4 and 6<\/font><\/p>\n

Is 18 a common multiple of 6 and 7 ? The\n answer is no, as though
\n 6 x 3 = 18, 7 cannot be multiplied by any number to give\n 18, so 18 is not a multiple of 7, though it is of 6.<\/font><\/p>\n

Least Common Multiple (LCM)
\n <\/u>As the name suggests the LCM of two numbers is the\n smallest number which is a multiple of both numbers.<\/font><\/p>\n

Method for Finding LCM
\n <\/u>Let us take two numbers 6 and 9<\/font><\/p>\n