Question

How do you find all the factors of 77?

Answer 1

Hint: Factors of a number are defined as all the possible sets of two numbers whose product is equal to the given number. For example, let us find the factors of 10, we know that 10 is equal to the product of 2 and 5, and 10 and 1 so these are the two factors of 10, but we also know that a negative number multiplied with another negative number gives a positive number, so -2 and -5, and -1 and -10 are also the factors of 10. Thus, the factors of 10 are 1, 2, 5, 10, -10, -5, -2, and -1. Following this approach, we can solve the given question.

Complete step-by-step answer:
Every number is divisible by 1 and itself, so 1 and 77 are the obvious factors of 77.
Now, 77 can be written as a product of 7 and 11; both of these numbers are prime numbers so they cannot be simplified further so the product of 7 and 11 is the only possible way to write 77.
We know that the product of two negative numbers is positive, so -1, -77, -11 and -7 are also the factors of 77.
Hence all the factors of 77 are 1, 7, 11, 77, -1, -7, -11, and -77.
So, the correct answer is “1, 7, 11, 77, -1, -7, -11, and -77”.

Note: By factorizing a number we mean to express it as a product of two numbers or it can also be defined as the division of a given number by some other number such that the remainder is zero. We usually don’t consider negative factors of a number and the fractions can never be considered as a factor of a number.