Factors of 98

The numbers that divide 98 evenly are known as factors of 98. A factor of 98 is a number that divides the number without remainder. The factors of 98 are 1, 2, 7, 14, 49, and 98.

Negative factors of 98: -1, -2, -7, -14, -49, and -98.

Prime factors of 98: 2 and 7.

Prime factorization of 98: 2 × 7².

The sum of factors of 98: 1 + 2 + 7 + 14 + 49 + 98 = 171

Factors can be found using different methods. Mentioned below are some commonly used methods:

• Finding factors using multiplication
• Finding factors using division method
• Prime factors and prime factorization

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 98. Identifying the numbers which are multiplied to get the number 98 is the multiplication method.

Step 1: Multiply 98 by 1, 98 × 1 = 98.

Step 2: Check for other numbers that give 98 after multiplying 2 × 49 = 98

7 × 14 = 98

Therefore, the positive factor pairs of 98 are: (1, 98), (2, 49), (7, 14).

All these factor pairs result in 98. For every positive factor, there is a negative factor.

Dividing the given numbers with whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following a simple division method -

Step 1: Divide 98 by 1, 98 ÷ 1 = 98.

Step 2: Continue dividing 98 by the numbers until the remainder becomes 0.

98 ÷ 1 = 98

98 ÷ 2 = 49

98 ÷ 7 = 14

Therefore, the factors of 98 are: 1, 2, 7, 14, 49, 98.

The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:

• Using prime factorization
• Using factor tree

Using Prime Factorization: In this process, prime factors of 98 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.

98 ÷ 2 = 49

49 ÷ 7 = 7

7 ÷ 7 = 1

The prime factors of 98 are 2 and 7. The prime factorization of 98 is: 2 × 7².

The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -

Step 1: Firstly, 98 is divided by 2 to get 49.

Step 2: Now divide 49 by 7 to get 7.

Step 3: Divide 7 by 7 to get 1. Here, we reach 1, and all the factors are prime numbers. So, the prime factorization of 98 is: 2 × 7².

Factor Pairs: Two numbers that are multiplied to give a specific number are called factor pairs. Both positive and negative factors constitute factor pairs.

• Positive factor pairs of 98: (1, 98), (2, 49), (7, 14).
• Negative factor pairs of 98: (-1, -98), (-2, -49), (-7, -14).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 98 are 1, 2, 7, 14, 49, and 98.

• Prime factors: The factors which are prime numbers. For example, 2 and 7 are prime factors of 98.

• Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 98 are (1, 98), (2, 49), etc.

• Prime factorization: Breaking down a number into its prime factors. For 98, it is 2 × 7².

• Multiplication method: A way to find factors by identifying pairs of numbers that multiply to the original number. For example, using pairs like (7, 14) for 98.