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Factors of 2704

Factors of 2704 are the list of integers that can be evenly divided into 2704. There are overall 15 factors of 2704, of which 2, 13 are its prime factors. The sum of all factors of 2704 is 5673.

All Factors of 2704: 1, 2, 4, 8, 13, 16, 26, 52, 104, 169, 208, 338, 676, 1352 and 2704
Prime Factors of 2704: 2, 13
Prime Factorization of 2704: 2⁴ × 13²
Sum of Factors of 2704: 5673

1.	What Are the Factors of 2704?
2.	Factors of 2704 by Prime Factorization
3.	Factors of 2704 in Pairs
4.	FAQs on Factors of 2704

What are Factors of 2704?

Factors of 2704 are pairs of those numbers whose products result in 2704. These factors are either prime numbers or composite numbers.

How to Find the Factors of 2704?

To find the factors of 2704, we will have to find the list of numbers that would divide 2704 without leaving any remainder.

2704/52 = 52; therefore, 52 is a factor of 2704.
2704/208 = 13; therefore, 208 is a factor of 2704 and 13 is also a factor of 2704.

Similarly we can find other factors. Hence, the factors of 2704 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 169, 208, 338, 676, 1352, 2704.

☛ Also Check:

Factors of 22 - The factors of 22 are 1, 2, 11, 22
Factors of 35 - The factors of 35 are 1, 5, 7, 35
Factors of 80 - The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
Factors of 180 - The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
Factors of 6 - The factors of 6 are 1, 2, 3, 6

Factors of 2704 by Prime Factorization

The number 2704 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 2704. The first step is to divide the number 2704 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.

2704 ÷ 2 = 1352
1352 ÷ 2 = 676
676 ÷ 2 = 338
338 ÷ 2 = 169

Further dividing 169 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 169 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 2704 can be written as 2⁴ × 13² where 2, 13 are prime.

Factors of 2704 in Pairs

Pair factors of 2704 are the pairs of numbers that when multiplied give the product 2704. The factors of 2704 in pairs are:

1 × 2704 = (1, 2704)
2 × 1352 = (2, 1352)
4 × 676 = (4, 676)
8 × 338 = (8, 338)
13 × 208 = (13, 208)
16 × 169 = (16, 169)
26 × 104 = (26, 104)
52 × 52 = (52, 52)

Negative pair factors of 2704 are:

-1 × -2704 = (-1, -2704)
-2 × -1352 = (-2, -1352)
-4 × -676 = (-4, -676)
-8 × -338 = (-8, -338)
-13 × -208 = (-13, -208)
-16 × -169 = (-16, -169)
-26 × -104 = (-26, -104)
-52 × -52 = (-52, -52)

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

Factors of 2704 Solved Examples

Example 1: How many factors are there for 2704?

Solution:

The factors of 2704 are too many, therefore if we can find the prime factorization of 2704, 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 2704 = 2⁴ × 13²
Therefore, the total number of factors are (4 + 1) × (2 + 1) = 5 × 3 = 15
Example 2: Find the LCM and Greatest Common Factor (GCF) of 2704 and 1220.

Solution:

The factors of 2704 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 169, 208, 338, 676, 1352, 2704 and factors of 1220 are 1, 2, 4, 5, 10, 20, 61, 122, 244, 305, 610, 1220.

Therefore, the LCM of 2704 and 1220 is 824720 and Greatest Common Factor (GCF) of 2704 and 1220 is 4.
Example 3: Find if 2, 13, 16, 52, 185, 208, 338 and 676 are factors of 2704.

Solution:

When we divide 2704 by 185 it leaves a remainder. Therefore, the number 185 is not a factor of 2704. All numbers except 185 are factors of 2704.
Example 4: Find the product of all the prime factors of 2704.

Solution:

Since, the prime factors of 2704 are 2, 13. Therefore, the product of prime factors = 2 × 13 = 26.

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FAQs on Factors of 2704

What are the Factors of 2704?

The factors of 2704 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 169, 208, 338, 676, 1352, 2704 and its negative factors are -1, -2, -4, -8, -13, -16, -26, -52, -104, -169, -208, -338, -676, -1352, -2704.

What is the Sum of all Factors of 2704?

Sum of all factors of 2704 = (2^{4 + 1} - 1)/(2 - 1) × (13^{2 + 1} - 1)/(13 - 1) = 5673

What Numbers are the Prime Factors of 2704?

The prime factors of 2704 are 2, 13.

What is the Greatest Common Factor of 2704 and 955?

The factors of 2704 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 169, 208, 338, 676, 1352, 2704 and the factors of 955 are 1, 5, 191, 955. 2704 and 955 have only one common factor which is 1. This implies that 2704 and 955 are co-prime.

Hence, the Greatest Common Factor (GCF) of 2704 and 955 is 1.

How Many Factors of 2704 are also common to the Factors of 1697?

Since, the factors of 2704 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 169, 208, 338, 676, 1352, 2704 and factors of 1697 are 1, 1697. Hence, 2704 and 1697 have only one common factor which is 1. Therefore, 2704 and 1697 are co-prime.

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