What are the factors of 100

General
1

what are the factors of 100

2

What are the factors of 100?

Answer:

To determine the factors of 100, let’s begin by explaining what a factor is. A factor is a number that divides into another number without leaving a remainder. That means if you multiply two whole numbers together to get a product, both of those numbers are factors of the product.

Step-by-Step Factorization of 100

  1. Start with the smallest number:

    • 1 is a factor of every number, including 100. So, 1 multiplied by 100 gives us 100. Thus, (1, 100) is a pair of factors.

  2. Proceed to the next smallest numbers:

    • Check if 100 is divisible by 2. Since 100 is even, it is divisible by 2. When you divide 100 by 2, you get 50. Therefore, (2, 50) is another pair of factors.

  3. Continue with the next integers:

    • 100 divided by 3 does not yield a whole number (100 ÷ 3 = 33.33…), so 3 is not a factor.
    • 100 divided by 4 does yield a whole number (100 ÷ 4 = 25), so (4, 25) is a factor pair.
    • 100 divided by 5 yields 20 (100 ÷ 5 = 20), so (5, 20) is a factor pair.
    • 100 divided by 6 does not yield a whole number (100 ÷ 6 = 16.67…), so 6 is not a factor.
    • 100 divided by 7 does not yield a whole number (100 ÷ 7 ≈ 14.29), so 7 is not a factor.
    • 100 divided by 8 does not yield a whole number (100 ÷ 8 = 12.5), so 8 is not a factor.
    • 100 divided by 9 does not yield a whole number (100 ÷ 9 ≈ 11.111…), so 9 is not a factor.
    • 100 divided by 10 yields a whole number (100 ÷ 10 = 10), so (10, 10) is a factor. Note that this pair is a square root pair.

Listing All Factors

After examining key integers, the complete list of factors of 100 are:
1, 2, 4, 5, 10, 20, 25, 50, 100

These include all whole numbers that can multiply with another whole number to produce the product 100.

Prime Factorization of 100

For additional insight, let’s look at the prime factorization of 100.

  1. Start by dividing 100 by its smallest prime factor. Since 100 is even, we start with 2: ( 100 \div 2 = 50 ).
  2. Dividing 50 by 2 again: ( 50 \div 2 = 25 ).
  3. Now, 25 is not divisible by 2. The next smallest prime is 3 but it doesn’t divide evenly, so try 5: ( 25 \div 5 = 5 ).
  4. Finally, divide 5 by 5: ( 5 \div 5 = 1 ).

This can be expressed in exponential form for better visualization:
100 = ( 2^2 \times 5^2 ).

Thus, the prime factors of 100 are 2 and 5, and the factor pairs involving these primes help in constructing the full factors list from their combinations.

Understanding Factor Pairs

For clarity, each factor of 100 pairs with another:

  • (1, 100)
  • (2, 50)
  • (4, 25)
  • (5, 20)
  • (10, 10) (Notice how 10 pairs with itself because it is the square root of 100)

Factorization and understanding factor pairs are especially useful in real-world applications, such as simplifying fractions, calculating areas, or solving algebraic expressions where factorization is needed.

By systematically breaking down a number into its factors, you gain deeper insight into the structure and composition of that number, which can also aid in solving problems relating to divisibility and number theory.