Playing With Numbers

While solving these sums we need to keep certain formulas and definition at first :-

  • Firstly, we need to keep in mind the definition of a factor. A factor is a number which exactly divides a number. Every number has a few fixed factors. The number itself and one is a factor of every number.
  • Secondly, a perfect number is a number in which the sum of all the numbers factors is equal to twice the number.
  • Thirdly, prime number are number which have only one and the number itself as the only factors.
  • Fourthly, composite numbers are numbers which have more than two factors. It is also important to know that one is neither a prime nor composite number.
  • Fifthly, even numbers are all the numbers which are divisible by two.
  • Sixthly, all the other numbers except for even numbers are called odd numbers. It is also important to know that two is the only prime number that is even. Also, that all the prime numbers other than two are odd numbers in general. There is one important rule to test for divisibility of numbers. If the number has zero as the last digit it is divisible by ten. Also, if the number has five or zero as the last digit then the number is likely divisible by five. Another rule is that a number is divisible by two if it has any even number as the last digit. A number is divisible by three if the sum of the individual digits of the number is divisible by three.
  • Seventhly, two numbers having only one as the common factor in between them are called co – prime numbers. LCM of a number is the smallest of the common multiples of the number. The HCF of a number is the greatest of the common multiples of the number.

Example: What is the prime factorization of {72}

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Therefore, the prime factorization is {2 \times 2 \times 2 \times 3 \times 3}

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