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A number which is a factor of every number is ___. a). 0 b). 1 c). 2 d). 5

A number which is a factor of every number is ___.
a). 0
b). 1
c). 2
d). 5

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 9723 Points
21 days ago
For solving this problem, we use the definition of factors of a number. The largest number that divides two or more numbers is the highest common factor (HCF). Now, we can easily calculate the required thing. Complete step-by-step solution - Factors: All the numbers that divide a number completely, i.e., without leaving any remainder, are called factors of that number. Multiples are those numbers which on multiplication gives the desired number. All these multiples individually can be named as a factor of the given number. To find the factors of any given number, we express each number as a product of prime numbers since they do not leave any remainder. For example, consider some numbers such as 1, 8, 21, 29. So, the factor of 1 is 1. The factors of 8 are 1, 2, 4 and 8. The factors of 29 are 1 and 29. From these calculations, we observe that 1 is the greatest factor of itself and the smallest factor of any other number. Therefore, 1 is the factor of every number. Hence, option (b) is correct. Note: This problem is a direct problem in which the knowledge of factors of a number is required. This knowledge is essential to solve complex problems related to the topic. Students must be aware of the facts associated with number 1.

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