1. Steps to find factors of 448 using Division Method

Example: Find factors of 448

  • Divide 448 by 1: 448 ÷ 1 : Remainder = 0
  • Divide 448 by 2: 448 ÷ 2 : Remainder = 0
  • Divide 448 by 4: 448 ÷ 4 : Remainder = 0
  • Divide 448 by 7: 448 ÷ 7 : Remainder = 0
  • Divide 448 by 8: 448 ÷ 8 : Remainder = 0
  • Divide 448 by 14: 448 ÷ 14 : Remainder = 0
  • Divide 448 by 16: 448 ÷ 16 : Remainder = 0
  • Divide 448 by 28: 448 ÷ 28 : Remainder = 0
  • Divide 448 by 32: 448 ÷ 32 : Remainder = 0
  • Divide 448 by 56: 448 ÷ 56 : Remainder = 0
  • Divide 448 by 64: 448 ÷ 64 : Remainder = 0
  • Divide 448 by 112: 448 ÷ 112 : Remainder = 0
  • Divide 448 by 224: 448 ÷ 224 : Remainder = 0
  • Divide 448 by 448: 448 ÷ 448 : Remainder = 0

Hence, Factors of 448 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, and 448

2. Steps to find factors of 448 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 448 using the division method, follow these steps:

  • Step 1. Start dividing 448 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 448, which is 2. Divide 448 by 2 to obtain the quotient (224).
    448 ÷ 2 = 224
  • Step 3. Repeat step 1 with the obtained quotient (224).
    224 ÷ 2 = 112
    112 ÷ 2 = 56
    56 ÷ 2 = 28
    28 ÷ 2 = 14
    14 ÷ 2 = 7
    7 ÷ 7 = 1

So, the prime factorization of 448 is, 448 = 2 x 2 x 2 x 2 x 2 x 2 x 7.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 448 as shown below:

So, the prime factorization of 448 is, 448 = 2 x 2 x 2 x 2 x 2 x 2 x 7.

3. Find factors of 448 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 448 would be the two numbers which, when multiplied, give 448 as the result.

The following table represents the calculation of factors of 448 in pairs:

Factor Pair Pair Factorization
1 and 448 1 x 448 = 448
2 and 224 2 x 224 = 448
4 and 112 4 x 112 = 448
7 and 64 7 x 64 = 448
8 and 56 8 x 56 = 448
14 and 32 14 x 32 = 448
16 and 28 16 x 28 = 448

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 448. They are called negative pair factors.

Hence, the negative pairs of 448 would be ( -1 , -448 ) , ( -2 , -224 ) , ( -4 , -112 ) , ( -7 , -64 ) , ( -8 , -56 ) , ( -14 , -32 ) and ( -16 , -28 ) .

What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

Properties of factors

  • Each number is a factor of itself. Eg. 448 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 448.
  • Every number is a factor of zero (0), since 448 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, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, 448 are exact divisors of 448.
  • Factors of 448 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, 448. Each factor divides 448 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, 448 are all less than or equal to 448.

Frequently Asked Questions

  • Which is the smallest prime factor of 448?

    The smallest prime factor of 448 is 2.

  • Is 448 a whole number?

    Yes 448 is a whole number.

  • What are the prime factors of 448?

    The factors of 448 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, 448.
    Prime factors of 448 are 2, 2, 2, 2, 2, 2, 7.

  • What two numbers make 448?

    Two numbers that make 448 are 2 and 224.

  • What are multiples of 448?

    First five multiples of 448 are 896, 1344, 1792, 2240.

  • What is the sum of all factors of 448?

    The sum of all factors of 448 is 1016.

  • What are five multiples of 448?

    First five multiples of 448 are 896, 1344, 1792, 2240, 2688.

  • Is 448 a perfect square?

    No 448 is not a perfect square.

  • What is the greatest prime factors of 448?

    The greatest prime factor of 448 is 7.

Examples of Factors

How many factors are there for 448?

Factors of 448 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, 448.
So there are in total 14 factors.

Kevin has been asked to write 13 factor(s) of 448. Can you predict the answer?

13 factor(s) of 448 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224.

Sammy is puzzled while calculating the prime factors of 448. Can you help him find them?

Factors of 448 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, 448.
Prime factors of 448 are 2, 2, 2, 2, 2, 2, 7

What is prime factorization of 448?

Prime factorization of 448 is 2 x 2 x 2 x 2 x 2 x 2 x 7 = 26 x 7.

Ariel has been assigned the task to find the product of all the prime factors of 448. Can you help her?

Prime factors of 448 are 2, 2, 2, 2, 2, 2, 7.
Hence, the product of prime factors of 14.

Can you help Rubel to find out the product of the even factors of 448?

Factors of 448 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, 448.
Even factors of 448 are 2, 4, 8, 14, 16, 28, 32, 56, 64, 112, 224, 448.
Hence, product of even factors of 448 is; 2 x 4 x 8 x 14 x 16 x 28 x 32 x 56 x 64 x 112 x 224 x 448 = 517425773984874500.

Joy wants to calculate mean of all the factors of 448. Help him in finding the mean of 448.

Factors of 448 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, 448.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 448 is 1 + 2 + 4 + 7 + 8 + 14 + 16 + 28 + 32 + 56 + 64 + 112 + 224 + 448 = 1016.
Hence, the mean of factors of 448 is 1016 ÷ 14 = 72.57.