Factors of 32

Factors of 32 are those numbers that, when multiplied together, give the result of 32. We can also say that a factor is a number that divides a number ultimately, leaving zero as a remainder. We will use the multiplication method to find the factors of 32.

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Factors of 32 Details

Factors of 32: 1, 2, 4, 8, 16 and 32
Factors of -32: -1, -2, -4, -8, -16 and -32
Prime Factors of 32: 2
Prime Factorization of 32: 2 × 2 × 2 × 2 × 2 = 25
Factors of 32 in Pairs: (1, 32), (2, 16) and (4, 8)
Negative Pairs Factors of 32: (-1, -32), (-2, -16) and (-4, -8)

What are the factors of 32?

The method of calculating the factors of 32 is as follows. First, each number can be divided by one and by itself.

Consequently, 1 and 32 are the factors of 32.
By dividing a number by 1, 2, 3, 4… we can discover all its factors.

(i) 32 ÷ 1 = 32

This division gives the remainder 0 and so is divisible by 32. So please put them 1 and 32 in your factor list.

1, …….. 32

(ii) 32 ÷ 2 = 16

This division gives the remainder 0 and so is divisible by 16. So please put them 2 and 16 in your factor list.

1, 2 …….. 16, 32

(iii) 32 ÷ 3 = 10.66

This division gives the remainder 10.66, not being thoroughly divided. So we will not write 3 and 10.66 on the list.

(iv) 32 ÷ 4 = 8

This division gives the remainder 0 and so is divisible by 8. So please put them 2 and 8 in your factor list.

1, 2, 4 …….. 8, 14, 32

(iv) 32 ÷ 5 = 6.4

This division gives the remainder 6.4, not being thoroughly divided. So we will not write 5 and 6.4 on the list.

(vi) Since we don’t have any more numbers to calculate, we are putting the numbers so far.

So 1, 2, 4, 8, 16 and 32 are factors of 32.

Factors of -32

To get the factors of -32 by the multiplication method, we will first write the number -32 multiplicatively in all possible ways. We can write -32 as follows and we have:

32 = -1 × -32 Therefor, -1, -32 are factors of -32
32 = -2 × -16 Therefor, -2, -16 are factors of -32
32 = -4 × -8 Therefor, -4, -8 are factors of -32

As there are no other ways we can express -32 multiplicative, we will stop now, and we have obtained all the factors of -32.

So, the factors of -32 are -1, -2, -4, -8, -16 and -32.

All factors of 32

Here is a list of all the positive and negative factors of 32 in numerical order.

1, 2, 4, 8, 16, 32, -1, -2, -4, -8, -16 and -32

Therefore, 1, 2, 4, 8, 16, 32, -1, -2, -4, -8, -16 and -32 are All factors of 32.

Factor pairs of 32

1 x 32 = 32
2 x 16 = 32
4 x 8 = 32

So, (1, 32), (2, 16) and (4, 8) are factor pairs of 32

Factor pairs of -32

-1 x -32 = 32
-2 x -16 = 32
-4 x -8 = 32

So, (-1, -32), (-2, -16) and (-4, -8) are negative pair factors of 32

Prime Factorization of 32

To find the prime factorization of a number, you need to express it as the product of its prime factors.

Prime numbers are numbers that are divisible only by 1 and themselves. Some examples of prime numbers are 2, 3, 5, 7, 11, 13, and so on.

To find the prime factorization of 32, we start by dividing it by the smallest prime number, which is 2. 32 divided by 2 is 16, with a remainder of 0. This means that 2 is a factor of 32. We can then divide 16 by 2, which gives us 8 with a remainder of 0. We can continue dividing by 2 until we get a quotient of 1:

32 ÷ 2 = 16 (remainder 0)
16 ÷ 2 = 8 (remainder 0)
8 ÷ 2 = 4 (remainder 0)
4 ÷ 2 = 2 (remainder 0)
2 ÷ 2 = 1 (remainder 0)

So, the prime factorization of 32 is 2 x 2 x 2 x 2 x 2, or 2^5.

Factor tree of 32

         32
        /   \
       2    16
            /    \
          2      8
                /    \
              2      4
                    /   \
                  2      2