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Factors of 3200

Factors of 3200 are numbers that, when multiplied in pairs give the product as 3200. There are 24 factors of 3200, of which the following are its prime factors 2, 5. The Prime Factorization of 3200 is 2⁷ × 5².

All Factors of 3200: 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 320, 400, 640, 800, 1600 and 3200
Prime Factors of 3200: 2, 5
Prime Factorization of 3200: 2⁷ × 5²
Sum of Factors of 3200: 7905

1.	What Are the Factors of 3200?
2.	Factors of 3200 by Prime Factorization
3.	Factors of 3200 in Pairs
4.	FAQs on Factors of 3200

What are Factors of 3200?

Factors of 3200 are pairs of those numbers whose products result in 3200. These factors are either prime numbers or composite numbers.

How to Find the Factors of 3200?

To find the factors of 3200, we will have to find the list of numbers that would divide 3200 without leaving any remainder.

3200/800 = 4; therefore, 800 is a factor of 3200 and 4 is also a factor of 3200.
3200/400 = 8; therefore, 400 is a factor of 3200 and 8 is also a factor of 3200.

Similarly we can find other factors. Hence, the factors of 3200 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 320, 400, 640, 800, 1600, 3200.

☛ Also Check:

Factors of 84 - The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Factors of 20 - The factors of 20 are 1, 2, 4, 5, 10, 20
Factors of 13 - The factors of 13 are 1, 13
Factors of 27 - The factors of 27 are 1, 3, 9, 27
Factors of 55 - The factors of 55 are 1, 5, 11, 55

Factors of 3200 by Prime Factorization

The number 3200 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 3200. The first step is to divide the number 3200 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.

3200 ÷ 2 = 1600
1600 ÷ 2 = 800
800 ÷ 2 = 400
400 ÷ 2 = 200
200 ÷ 2 = 100
100 ÷ 2 = 50
50 ÷ 2 = 25

Further dividing 25 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 25 by the next smallest prime factor. We stop ultimately if the next prime factor doesn't exist or when we can't divide any further.

So, the prime factorization of 3200 can be written as 2⁷ × 5² where 2, 5 are prime.

Factors of 3200 in Pairs

Pair factors of 3200 are the pairs of numbers that when multiplied give the product 3200. The factors of 3200 in pairs are:

1 × 3200 = (1, 3200)
2 × 1600 = (2, 1600)
4 × 800 = (4, 800)
5 × 640 = (5, 640)
8 × 400 = (8, 400)
10 × 320 = (10, 320)
16 × 200 = (16, 200)
20 × 160 = (20, 160)
25 × 128 = (25, 128)
32 × 100 = (32, 100)
40 × 80 = (40, 80)
50 × 64 = (50, 64)

Negative pair factors of 3200 are:

-1 × -3200 = (-1, -3200)
-2 × -1600 = (-2, -1600)
-4 × -800 = (-4, -800)
-5 × -640 = (-5, -640)
-8 × -400 = (-8, -400)
-10 × -320 = (-10, -320)
-16 × -200 = (-16, -200)
-20 × -160 = (-20, -160)
-25 × -128 = (-25, -128)
-32 × -100 = (-32, -100)
-40 × -80 = (-40, -80)
-50 × -64 = (-50, -64)

NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.

Factors of 3200 Solved Examples

Example 1: How many factors are there for 3200?

Solution:

The factors of 3200 are too many, therefore if we can find the prime factorization of 3200, then the total number of factors can be calculated using the formula shown below.
If the prime factorization of the number is a^x × b^y × c^z where a, b, c are prime, then the total number of factors can be given by (x + 1)(y + 1)(z + 1).

Prime Factorization of 3200 = 2⁷ × 5²
Therefore, the total number of factors are (7 + 1) × (2 + 1) = 8 × 3 = 24
Example 2: Find the Least Common Multiple (LCM) and Greatest Common Factor (GCF) of 3200 and 2815.

Solution:

The factors of 3200 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 320, 400, 640, 800, 1600, 3200 and factors of 2815 are 1, 5, 563, 2815.

Therefore, the Least Common Multiple (LCM) of 3200 and 2815 is 1801600 and Greatest Common Factor (GCF) of 3200 and 2815 is 5.
Example 3: Find if 2, 5, 8, 16, 20, 34, 64 and 3200 are factors of 3200.

Solution:

When we divide 3200 by 34 it leaves a remainder. Therefore, the number 34 is not a factor of 3200. All numbers except 34 are factors of 3200.
Example 4: Find the product of all the prime factors of 3200.

Solution:

Since, the prime factors of 3200 are 2, 5. Therefore, the product of prime factors = 2 × 5 = 10.

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FAQs on Factors of 3200

What are the Factors of 3200?

The factors of 3200 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 320, 400, 640, 800, 1600, 3200 and its negative factors are -1, -2, -4, -5, -8, -10, -16, -20, -25, -32, -40, -50, -64, -80, -100, -128, -160, -200, -320, -400, -640, -800, -1600, -3200.

What is the Sum of all Factors of 3200?

Sum of all factors of 3200 = (2^{7 + 1} - 1)/(2 - 1) × (5^{2 + 1} - 1)/(5 - 1) = 7905

What are the Prime Factors of 3200?

The prime factors of 3200 are 2, 5.

What is the Greatest Common Factor of 3200 and 377?

The factors of 3200 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 320, 400, 640, 800, 1600, 3200 and the factors of 377 are 1, 13, 29, 377. 3200 and 377 have only one common factor which is 1. This implies that 3200 and 377 are co-prime.

Hence, the Greatest Common Factor (GCF) of 3200 and 377 is 1.

How Many Factors of 3200 are also Factors of 2144?

Since, the factors of 3200 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 320, 400, 640, 800, 1600, 3200 and the factors of 2144 are 1, 2, 4, 8, 16, 32, 67, 134, 268, 536, 1072, 2144.
Hence, [1, 2, 4, 8, 16, 32] are the common factors of 3200 and 2144.

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