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Factors of 3400

Factors of 3400 are the list of integers that we can split evenly into 3400. There are overall 24 factors of 3400 among which 3400 is the biggest factor and 2, 5, 17 are its prime factors. The sum of all factors of 3400 is 8370.

All Factors of 3400: 1, 2, 4, 5, 8, 10, 17, 20, 25, 34, 40, 50, 68, 85, 100, 136, 170, 200, 340, 425, 680, 850, 1700 and 3400
Prime Factors of 3400: 2, 5, 17
Prime Factorization of 3400: 2³ × 5² × 17¹
Sum of Factors of 3400: 8370

1.	What Are the Factors of 3400?
2.	Factors of 3400 by Prime Factorization
3.	Factors of 3400 in Pairs
4.	FAQs on Factors of 3400

What are Factors of 3400?

Factors of 3400 are pairs of those numbers whose products result in 3400. These factors are either prime numbers or composite numbers.

How to Find the Factors of 3400?

To find the factors of 3400, we will have to find the list of numbers that would divide 3400 without leaving any remainder.

3400/40 = 85; therefore, 40 is a factor of 3400 and 85 is also a factor of 3400.
3400/34 = 100; therefore, 34 is a factor of 3400 and 100 is also a factor of 3400.

Similarly we can find other factors. Hence, the factors of 3400 are 1, 2, 4, 5, 8, 10, 17, 20, 25, 34, 40, 50, 68, 85, 100, 136, 170, 200, 340, 425, 680, 850, 1700, 3400.

☛ Also Check:

Factors of 7 - The factors of 7 are 1, 7
Factors of 63 - The factors of 63 are 1, 3, 7, 9, 21, 63
Factors of 49 - The factors of 49 are 1, 7, 49
Factors of 25 - The factors of 25 are 1, 5, 25
Factors of 28 - The factors of 28 are 1, 2, 4, 7, 14, 28

Factors of 3400 by Prime Factorization

The number 3400 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 3400. The first step is to divide the number 3400 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.

3400 ÷ 2 = 1700
1700 ÷ 2 = 850
850 ÷ 2 = 425

Further dividing 425 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 425 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 3400 can be written as 2³ × 5² × 17¹ where 2, 5, 17 are prime.

Factors of 3400 in Pairs

Pair factors of 3400 are the pairs of numbers that when multiplied give the product 3400. The factors of 3400 in pairs are:

1 × 3400 = (1, 3400)
2 × 1700 = (2, 1700)
4 × 850 = (4, 850)
5 × 680 = (5, 680)
8 × 425 = (8, 425)
10 × 340 = (10, 340)
17 × 200 = (17, 200)
20 × 170 = (20, 170)
25 × 136 = (25, 136)
34 × 100 = (34, 100)
40 × 85 = (40, 85)
50 × 68 = (50, 68)

Negative pair factors of 3400 are:

-1 × -3400 = (-1, -3400)
-2 × -1700 = (-2, -1700)
-4 × -850 = (-4, -850)
-5 × -680 = (-5, -680)
-8 × -425 = (-8, -425)
-10 × -340 = (-10, -340)
-17 × -200 = (-17, -200)
-20 × -170 = (-20, -170)
-25 × -136 = (-25, -136)
-34 × -100 = (-34, -100)
-40 × -85 = (-40, -85)
-50 × -68 = (-50, -68)

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

Factors of 3400 Solved Examples

Example 1: How many factors are there for 3400?

Solution:

The factors of 3400 are too many, therefore if we can find the prime factorization of 3400, 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 3400 = 2³ × 5² × 17¹
Therefore, the total number of factors are (3 + 1) × (2 + 1) × (1 + 1) = 4 × 3 × 2 = 24
Example 2: Find the Least Common Multiple and Highest Common Factor (HCF) of 3400 and 2421.

Solution:

The factors of 3400 are 1, 2, 4, 5, 8, 10, 17, 20, 25, 34, 40, 50, 68, 85, 100, 136, 170, 200, 340, 425, 680, 850, 1700, 3400 and factors of 2421 are 1, 3, 9, 269, 807, 2421.

Therefore, the Least Common Multiple of 3400 and 2421 is 8231400 and Highest Common Factor (HCF) of 3400 and 2421 is 1.
Example 3: Find if 17, 50, 85, 100, 170, 425, 680 and 732 are factors of 3400.

Solution:

When we divide 3400 by 732 it leaves a remainder. Therefore, the number 732 is not a factor of 3400. All numbers except 732 are factors of 3400.
Example 4: Find the product of all the prime factors of 3400.

Solution:

Since, the prime factors of 3400 are 2, 5, 17. Therefore, the product of prime factors = 2 × 5 × 17 = 170.

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FAQs on Factors of 3400

What are the Factors of 3400?

The factors of 3400 are 1, 2, 4, 5, 8, 10, 17, 20, 25, 34, 40, 50, 68, 85, 100, 136, 170, 200, 340, 425, 680, 850, 1700, 3400 and its negative factors are -1, -2, -4, -5, -8, -10, -17, -20, -25, -34, -40, -50, -68, -85, -100, -136, -170, -200, -340, -425, -680, -850, -1700, -3400.

What is the Sum of all Factors of 3400?

Sum of all factors of 3400 = (2^{3 + 1} - 1)/(2 - 1) × (5^{2 + 1} - 1)/(5 - 1) × (17^{1 + 1} - 1)/(17 - 1) = 8370

What Numbers are the Prime Factors of 3400?

The prime factors of 3400 are 2, 5, 17.

What is the Greatest Common Factor of 3400 and 88?

The factors of 3400 and 88 are 1, 2, 4, 5, 8, 10, 17, 20, 25, 34, 40, 50, 68, 85, 100, 136, 170, 200, 340, 425, 680, 850, 1700, 3400 and 1, 2, 4, 8, 11, 22, 44, 88 respectively.

Common factors of 3400 and 88 are [1, 2, 4, 8].

Hence, the GCF of 3400 and 88 is 8.

How Many Factors of 3400 are also Factors of 303?

Since, the factors of 3400 are 1, 2, 4, 5, 8, 10, 17, 20, 25, 34, 40, 50, 68, 85, 100, 136, 170, 200, 340, 425, 680, 850, 1700, 3400 and factors of 303 are 1, 3, 101, 303. Hence, 3400 and 303 have only one common factor which is 1. Therefore, 3400 and 303 are co-prime.

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