Question

Write all the factors of: 98

Answer 1

Hint: A factor is a number that divides into another number exactly and without leaving a
remainder. Most numbers have an even number of factors; however, a square number has an odd number of factors. A prime number has only two factors - the number itself and 1. The quickest way to find the factors of a number is to divide it by the smallest prime number (bigger than 1) that goes into it evenly with no remainder. Continue this process with each number we get, until we reach 1.

Complete step-by-step answer:
Factors of a number are the product of such numbers which completely divide the given number. Factors of a given number can be either positive or negative numbers. By multiplying the factors of a number, we get the original number. For example, 1,2,3,6 are the factors of 6. On multiplying two or more numbers we get 6.
According to the definition of factors of 98, we know that factors of 98 are all the positive or negative integers which divide the number 98 completely. So, let us simply divide the number 98 by every number which completely divides 98 in ascending order till 98.
$98 \div 1=98$
$98 \div 2=49$
$98 \div 3=$ not divides completely $98 \div 4=$ not divide completely $98 \div 5=$ not divides completely $98 \div 6=$ not divides completely $98 \div 7=14$
$98 \div 14=7$
$98 \div 49=2$
$98 \div 98=1$
So, all factors of 98: 1,2,7,14,49, and 98.
We know that factors also include negative integers hence we can also have,
list of negative factors of $98:-1,-2,-7,-14,-49,$ and -98.

Note: All Factor Pairs of 98 are combinations of two factors that when multiplied together give 98.
List of all the positive pair factors of 98 $1 \times 98=98 ;(1,98)$
$2 \times 49=98 ;(2,49)$
$7 \times 14=98 ;(7,14)$
So $(1,98),(2,49),$ and (7,14) are the positive pair factors of 98
As we know that Factors of 98 include negative integers too. List of all the negative pair factors of 98:
$-1 *-98=98$
$-2 *-49=98$
$-7 *-14=98$
So $(-1,-98),(-2,-49),$ and (-7, -14) are the negative pair factors of 98