1. Steps to find factors of 416 using Division Method

Example: Find factors of 416

  • Divide 416 by 1: 416 ÷ 1 : Remainder = 0
  • Divide 416 by 2: 416 ÷ 2 : Remainder = 0
  • Divide 416 by 4: 416 ÷ 4 : Remainder = 0
  • Divide 416 by 8: 416 ÷ 8 : Remainder = 0
  • Divide 416 by 13: 416 ÷ 13 : Remainder = 0
  • Divide 416 by 16: 416 ÷ 16 : Remainder = 0
  • Divide 416 by 26: 416 ÷ 26 : Remainder = 0
  • Divide 416 by 32: 416 ÷ 32 : Remainder = 0
  • Divide 416 by 52: 416 ÷ 52 : Remainder = 0
  • Divide 416 by 104: 416 ÷ 104 : Remainder = 0
  • Divide 416 by 208: 416 ÷ 208 : Remainder = 0
  • Divide 416 by 416: 416 ÷ 416 : Remainder = 0

Hence, Factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, and 416

2. Steps to find factors of 416 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 416 using the division method, follow these steps:

  • Step 1. Start dividing 416 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 416, which is 2. Divide 416 by 2 to obtain the quotient (208).
    416 ÷ 2 = 208
  • Step 3. Repeat step 1 with the obtained quotient (208).
    208 ÷ 2 = 104
    104 ÷ 2 = 52
    52 ÷ 2 = 26
    26 ÷ 2 = 13
    13 ÷ 13 = 1

So, the prime factorization of 416 is, 416 = 2 x 2 x 2 x 2 x 2 x 13.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 416 as shown below:

So, the prime factorization of 416 is, 416 = 2 x 2 x 2 x 2 x 2 x 13.

3. Find factors of 416 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 416 would be the two numbers which, when multiplied, give 416 as the result.

The following table represents the calculation of factors of 416 in pairs:

Factor Pair Pair Factorization
1 and 416 1 x 416 = 416
2 and 208 2 x 208 = 416
4 and 104 4 x 104 = 416
8 and 52 8 x 52 = 416
13 and 32 13 x 32 = 416
16 and 26 16 x 26 = 416

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 416. They are called negative pair factors.

Hence, the negative pairs of 416 would be ( -1 , -416 ) , ( -2 , -208 ) , ( -4 , -104 ) , ( -8 , -52 ) , ( -13 , -32 ) and ( -16 , -26 ) .

How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

Properties of factors

  • Each number is a factor of itself. Eg. 416 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 416.
  • Every number is a factor of zero (0), since 416 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, 8, 13, 16, 26, 32, 52, 104, 208, 416 are exact divisors of 416.
  • Factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416. Each factor divides 416 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416 are all less than or equal to 416.

Frequently Asked Questions

  • What two numbers make 416?

    Two numbers that make 416 are 2 and 208.

  • What is prime factorization of 416?

    Prime factorization of 416 is 2 x 2 x 2 x 2 x 2 x 13.

  • Write some multiples of 416?

    First five multiples of 416 are 832, 1248, 1664, 2080.

  • Which is the smallest prime factor of 416?

    The smallest prime factor of 416 is 2.

  • Is 416 a perfect square?

    No 416 is not a perfect square.

  • What is the sum of all factors of 416?

    The sum of all factors of 416 is 882.

  • What are factors of 416?

    Factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416.

  • How do you find factors of a negative number? ( eg. -416 )?

    Factors of -416 are -1, -2, -4, -8, -13, -16, -26, -32, -52, -104, -208, -416.

  • Is 416 a whole number?

    Yes 416 is a whole number.

Examples of Factors

Joy wants to calculate mean of all the factors of 416. Help him in finding the mean of 416.

Factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 416 is 1 + 2 + 4 + 8 + 13 + 16 + 26 + 32 + 52 + 104 + 208 + 416 = 882.
Hence, the mean of factors of 416 is 882 ÷ 12 = 73.50.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 416? Help her in writing all the factors.

Positive factors are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416.
Negative factors are -1, -2, -4, -8, -13, -16, -26, -32, -52, -104, -208, -416.

Joey wants to write all the prime factors of 416 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 416 are 2, 2, 2, 2, 2, 13.
So in exponential form it can be written as 25 x 13.

Kevin has been asked to write 11 factor(s) of 416. Can you predict the answer?

11 factor(s) of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208.

Sammy is puzzled while calculating the prime factors of 416. Can you help him find them?

Factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416.
Prime factors of 416 are 2, 2, 2, 2, 2, 13

What is prime factorization of 416?

Prime factorization of 416 is 2 x 2 x 2 x 2 x 2 x 13 = 25 x 13.

Can you help Rubel to find out the product of the even factors of 416?

Factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416.
Even factors of 416 are 2, 4, 8, 16, 26, 32, 52, 104, 208, 416.
Hence, product of even factors of 416 is; 2 x 4 x 8 x 16 x 26 x 32 x 52 x 104 x 208 x 416 = 398672823058432.