What are the factors of 21

General
1

what are the factors of 21

2

What are the factors of 21?

Answer:

To determine the factors of 21, we identify all the integers that can be multiplied together to result in the number 21. A factor is a whole number that divides another number completely without leaving a remainder.

Here’s how we can find the factors:

Step 1: Start with the number 1.

Every integer is divisible by 1, so 1 is always a factor. Hence, 1 is a factor of 21.

Step 2: Check the next whole numbers.

  • Divide by 2: Since 21 is an odd number, it is not divisible by 2. Therefore, 2 is not a factor of 21.

  • Divide by 3: The sum of the digits of 21 is (2 + 1 = 3), which is divisible by 3. Therefore, 21 is divisible by 3. Dividing 21 by 3 gives:

    $$ 21 \div 3 = 7 $$

    Therefore, 3 and 7 are factors of 21.

Step 3: Continue checking for other factors up to the square root of 21.

  • Divide by 4: (21 \div 4 \approx 5.25), not a whole number, so 4 is not a factor.
  • Divide by 5: Since 21 does not end in 0 or 5, it is not divisible by 5.
  • Divide by 6: (21 \div 6 \approx 3.5), not a whole number, so 6 is not a factor.

As we calculated above, the factors we have found are 1, 3, 7, and their pair factor 21 itself:

Factors of 21 are: 1, 3, 7, and 21.

For reference, a number’s factors can be determined generally by testing which whole numbers produce whole number results when divided into the given number. Furthermore, every factor pair (for instance, 3 and 7) when multiplied will yield the original number, 21.

Understanding Factor Pairs:

  • 1 x 21 = 21
  • 3 x 7 = 21

There are no other whole number combinations that multiply together to make 21 apart from these pairs.

Prime Factorization of 21:

To offer more insight, we can also consider the prime factorization of 21:

  • Start dividing by the smallest prime number, which is 2. Since 21 is odd, it’s not divisible by 2.

  • The next prime number is 3. Since 21 is divisible by 3, we perform the division:

    $$ 21 \div 3 = 7 $$

  • Next, we consider 7. Here, 7 is a prime number itself, so it stops the factorization process.

Thus, the prime factorization of 21 results in 3 and 7, both primes:

$$ 21 = 3 \times 7 $$

Each of these numbers (3 and 7) is a prime and appeared in our factor list, indicating that prime factorization results align with identified factors.

By thoroughly evaluating both basic factors and prime factorization, we not only identify the divisible integers connected to 21 but also confirm correctness and comprehension through different mathematics perspectives.