What Are The Factors Of 98

Julian Assange

less than a minute read

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10-12-2024

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Finding the factors of a number involves identifying all the numbers that divide evenly into that number without leaving a remainder. Let's break down how to find the factors of 98.

Method 1: Systematic Approach

We can start by systematically checking each number, starting from 1, to see if it divides evenly into 98:

• 1: 98 ÷ 1 = 98 (1 is always a factor)
• 2: 98 ÷ 2 = 49 (2 is a factor)
• 7: 98 ÷ 7 = 14 (7 is a factor)
• 14: 98 ÷ 14 = 7 (14 is a factor)
• 49: 98 ÷ 49 = 2 (49 is a factor)
• 98: 98 ÷ 98 = 1 (98 is always a factor)

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

Method 2: Prime Factorization

A more efficient method, especially for larger numbers, is prime factorization. This involves breaking down the number into its prime factors (numbers divisible only by 1 and themselves).

1. Start by dividing 98 by the smallest prime number, 2: 98 ÷ 2 = 49
2. Now, we have 49. 49 is not divisible by 2 or 3, but it is divisible by 7: 49 ÷ 7 = 7
3. 7 is a prime number.

So, the prime factorization of 98 is 2 x 7 x 7, or 2 x 7².

To find all the factors, we consider all possible combinations of these prime factors:

• 2¹ x 7⁰ = 2
• 2¹ x 7¹ = 14
• 2¹ x 7² = 98
• 2⁰ x 7¹ = 7
• 2⁰ x 7² = 49
• 2⁰ x 7⁰ = 1

This again gives us the factors 1, 2, 7, 14, 49, and 98.

Conclusion

Both methods lead to the same result: The factors of 98 are 1, 2, 7, 14, 49, and 98. Prime factorization is generally a more efficient approach for larger numbers.