Question

A certain composite number has 4 factors and the sum of them is 96. Find the number(hint the number is divisible by 7). Just don't give me the answer by guessing. show me how you arrived at the solution elaborately i.e. show me your working in detail

Answer 1

77

Explanation:

The first factor is 1

Since it is divisible by 7, 7 will also be one of its factors.

Therefore the four factors are

1, 7, x, y

When x and y are integers

Using the following law...

The product of factors of a number in the same position (left or right) (increasing or decreasing order) is equal to the number

Counting from left

y is the first factor

x is the second factor

Counting from the right

1 is the first factor

7 is the second factor

Applying the last

y×1=x×7

y = 7x

the sum of the factors is 96

1+7+x+7x = 96

8x+8=96

8x = 88

x= 11

Hence the number is

7x = 7(11)

=77

Answer 2

`\huge\boxed{77}`

Explanation:

The number can be divisible by 7.

The multiples of 7 are 7,14,21,28,35,42,49,56,63,70,77,84 and so on

Finding the factors for all of the multiples of 7:

7 => 1,7 [Not 4 factors]

14 => 1,2,7,14 [4 factors but Sum = 24]

21 => 1,3,7,21 [4 factors but Sum = 32]

28 => 1, 2, 4, 7, 14, 28 [Not 4]

35 => 1,5,7,35 [4 factors but Sum = 48]

42 => 1, 2, 3, 6, 7, 14, 21, 42 [Not 4]

49 => 1,7,49 [Not 4]

56 => 1, 2, 4, 7, 8, 14, 28, 56 [Not 4]

63 => 1, 3, 7, 9, 21, 63 [Not 4]

70 => 1, 2, 5, 7, 10, 14, 35, 70 [Not 4]

77 => 1, 7, 11, 77 [4 factors and Sum = 96]