1. Steps to find factors of 3400 using Division Method

Example: Find factors of 3400

  • Divide 3400 by 1: 3400 ÷ 1 : Remainder = 0
  • Divide 3400 by 2: 3400 ÷ 2 : Remainder = 0
  • Divide 3400 by 4: 3400 ÷ 4 : Remainder = 0
  • Divide 3400 by 5: 3400 ÷ 5 : Remainder = 0
  • Divide 3400 by 8: 3400 ÷ 8 : Remainder = 0
  • Divide 3400 by 10: 3400 ÷ 10 : Remainder = 0
  • Divide 3400 by 17: 3400 ÷ 17 : Remainder = 0
  • Divide 3400 by 20: 3400 ÷ 20 : Remainder = 0
  • Divide 3400 by 25: 3400 ÷ 25 : Remainder = 0
  • Divide 3400 by 34: 3400 ÷ 34 : Remainder = 0
  • Divide 3400 by 40: 3400 ÷ 40 : Remainder = 0
  • Divide 3400 by 50: 3400 ÷ 50 : Remainder = 0
  • Divide 3400 by 68: 3400 ÷ 68 : Remainder = 0
  • Divide 3400 by 85: 3400 ÷ 85 : Remainder = 0
  • Divide 3400 by 100: 3400 ÷ 100 : Remainder = 0
  • Divide 3400 by 136: 3400 ÷ 136 : Remainder = 0
  • Divide 3400 by 170: 3400 ÷ 170 : Remainder = 0
  • Divide 3400 by 200: 3400 ÷ 200 : Remainder = 0
  • Divide 3400 by 340: 3400 ÷ 340 : Remainder = 0
  • Divide 3400 by 425: 3400 ÷ 425 : Remainder = 0
  • Divide 3400 by 680: 3400 ÷ 680 : Remainder = 0
  • Divide 3400 by 850: 3400 ÷ 850 : Remainder = 0
  • Divide 3400 by 1700: 3400 ÷ 1700 : Remainder = 0
  • Divide 3400 by 3400: 3400 ÷ 3400 : Remainder = 0

Hence, 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, and 3400

2. Steps to find factors of 3400 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

Method 1: Division Method

To find the primefactors of 3400 using the division method, follow these steps:

  • Step 1. Start dividing 3400 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
  • Step 2. After finding the smallest prime factor of the number 3400, which is 2. Divide 3400 by 2 to obtain the quotient (1700).
    3400 ÷ 2 = 1700
  • Step 3. Repeat step 1 with the obtained quotient (1700).
    1700 ÷ 2 = 850
    850 ÷ 2 = 425
    425 ÷ 5 = 85
    85 ÷ 5 = 17
    17 ÷ 17 = 1

So, the prime factorization of 3400 is, 3400 = 2 x 2 x 2 x 5 x 5 x 17.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 3400 as shown below:

So, the prime factorization of 3400 is, 3400 = 2 x 2 x 2 x 5 x 5 x 17.

3. Find factors of 3400 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 3400 would be the two numbers which, when multiplied, give 3400 as the result.

The following table represents the calculation of factors of 3400 in pairs:

Factor Pair Pair Factorization
1 and 3400 1 x 3400 = 3400
2 and 1700 2 x 1700 = 3400
4 and 850 4 x 850 = 3400
5 and 680 5 x 680 = 3400
8 and 425 8 x 425 = 3400
10 and 340 10 x 340 = 3400
17 and 200 17 x 200 = 3400
20 and 170 20 x 170 = 3400
25 and 136 25 x 136 = 3400
34 and 100 34 x 100 = 3400
40 and 85 40 x 85 = 3400
50 and 68 50 x 68 = 3400

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 3400. They are called negative pair factors.

Hence, the negative pairs of 3400 would be ( -1 , -3400 ) , ( -2 , -1700 ) , ( -4 , -850 ) , ( -5 , -680 ) , ( -8 , -425 ) , ( -10 , -340 ) , ( -17 , -200 ) , ( -20 , -170 ) , ( -25 , -136 ) , ( -34 , -100 ) , ( -40 , -85 ) and ( -50 , -68 ) .

What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

Properties of factors

  • Each number is a factor of itself. Eg. 3400 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 3400.
  • Every number is a factor of zero (0), since 3400 x 0 = 0.
  • Every number other than 1 has at least two factors, namely the number itself and 1.
  • Every factor of a number is an exact divisor of that number, example 1, 2, 4, 5, 8, 10, 17, 20, 25, 34, 40, 50, 68, 85, 100, 136, 170, 200, 340, 425, 680, 850, 1700, 3400 are exact divisors of 3400.
  • 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. Each factor divides 3400 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 5, 8, 10, 17, 20, 25, 34, 40, 50, 68, 85, 100, 136, 170, 200, 340, 425, 680, 850, 1700, 3400 are all less than or equal to 3400.

Frequently Asked Questions

  • Which is the smallest prime factor of 3400?

    The smallest prime factor of 3400 is 2.

  • Is 3400 a whole number?

    Yes 3400 is a whole number.

  • What are the prime 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.
    Prime factors of 3400 are 2, 2, 2, 5, 5, 17.

  • What two numbers make 3400?

    Two numbers that make 3400 are 2 and 1700.

  • What are multiples of 3400?

    First five multiples of 3400 are 6800, 10200, 13600, 17000.

  • What is the sum of all factors of 3400?

    The sum of all factors of 3400 is 8370.

  • What are five multiples of 3400?

    First five multiples of 3400 are 6800, 10200, 13600, 17000, 20400.

  • Is 3400 a perfect square?

    No 3400 is not a perfect square.

  • What is the greatest prime factors of 3400?

    The greatest prime factor of 3400 is 17.

Examples of Factors

How many factors are there for 3400?

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.
So there are in total 24 factors.

Kevin has been asked to write 23 factor(s) of 3400. Can you predict the answer?

23 factor(s) 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.

Sammy is puzzled while calculating the prime factors of 3400. Can you help him find them?

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.
Prime factors of 3400 are 2, 2, 2, 5, 5, 17

What is prime factorization of 3400?

Prime factorization of 3400 is 2 x 2 x 2 x 5 x 5 x 17 = 23 x 52 x 17.

Ariel has been assigned the task to find the product of all the prime factors of 3400. Can you help her?

Prime factors of 3400 are 2, 2, 2, 5, 5, 17.
Hence, the product of prime factors of 170.

Can you help Rubel to find out the product of the even factors of 3400?

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.
Even factors of 3400 are 2, 4, 8, 10, 20, 34, 40, 50, 68, 100, 136, 170, 200, 340, 680, 850, 1700, 3400.
Hence, product of even factors of 3400 is; 2 x 4 x 8 x 10 x 20 x 34 x 40 x 50 x 68 x 100 x 136 x 170 x 200 x 340 x 680 x 850 x 1700 x 3400 = 3.1087100296429567e+34.

Joy wants to calculate mean of all the factors of 3400. Help him in finding the mean of 3400.

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.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 3400 is 1 + 2 + 4 + 5 + 8 + 10 + 17 + 20 + 25 + 34 + 40 + 50 + 68 + 85 + 100 + 136 + 170 + 200 + 340 + 425 + 680 + 850 + 1700 + 3400 = 8370.
Hence, the mean of factors of 3400 is 8370 ÷ 24 = 348.75.