# Factors of 424

Factors of 424 are 1, 2, 4, 8, 53, 106, 212, and 424

#### How to find factors of a number

 1.   Find factors of 424 using Division Method 2.   Find factors of 424 using Prime Factorization 3.   Find factors of 424 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 424

• Divide 424 by 1: 424 ÷ 1 : Remainder = 0
• Divide 424 by 2: 424 ÷ 2 : Remainder = 0
• Divide 424 by 4: 424 ÷ 4 : Remainder = 0
• Divide 424 by 8: 424 ÷ 8 : Remainder = 0
• Divide 424 by 53: 424 ÷ 53 : Remainder = 0
• Divide 424 by 106: 424 ÷ 106 : Remainder = 0
• Divide 424 by 212: 424 ÷ 212 : Remainder = 0
• Divide 424 by 424: 424 ÷ 424 : Remainder = 0

Hence, Factors of 424 are 1, 2, 4, 8, 53, 106, 212, and 424

#### 2. Steps to find factors of 424 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 424 using the division method, follow these steps:

• Step 1. Start dividing 424 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 424, which is 2. Divide 424 by 2 to obtain the quotient (212).
424 ÷ 2 = 212
• Step 3. Repeat step 1 with the obtained quotient (212).
212 ÷ 2 = 106
106 ÷ 2 = 53
53 ÷ 53 = 1

So, the prime factorization of 424 is, 424 = 2 x 2 x 2 x 53.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 424 as shown below:

So, the prime factorization of 424 is, 424 = 2 x 2 x 2 x 53.

#### 3. Find factors of 424 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 424 would be the two numbers which, when multiplied, give 424 as the result.

The following table represents the calculation of factors of 424 in pairs:

Factor Pair Pair Factorization
1 and 424 1 x 424 = 424
2 and 212 2 x 212 = 424
4 and 106 4 x 106 = 424
8 and 53 8 x 53 = 424

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 424. They are called negative pair factors.

Hence, the negative pairs of 424 would be ( -1 , -424 ) , ( -2 , -212 ) , ( -4 , -106 ) and ( -8 , -53 ) .

#### How can we define factors?

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

#### Properties of factors

• Each number is a factor of itself. Eg. 424 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 424.
• Every number is a factor of zero (0), since 424 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, 53, 106, 212, 424 are exact divisors of 424.
• Factors of 424 are 1, 2, 4, 8, 53, 106, 212, 424. Each factor divides 424 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 8, 53, 106, 212, 424 are all less than or equal to 424.

• What are the prime factors of 424?

The factors of 424 are 1, 2, 4, 8, 53, 106, 212, 424.
Prime factors of 424 are 2, 2, 2, 53.

• What is the sum of all factors of 424?

The sum of all factors of 424 is 810.

• What are the pair factors of 424?

Pair factors of 424 are (1,424), (2,212), (4,106), (8,53).

• What two numbers make 424?

Two numbers that make 424 are 2 and 212.

• What are multiples of 424?

First five multiples of 424 are 848, 1272, 1696, 2120.

• Is 424 a perfect square?

No 424 is not a perfect square.

• Which is greatest factor of 424?

The greatest factor of 424 is 212.

• How do you factors of 424?

Factors of 424 are 1, 2, 4, 8, 53, 106, 212, 424.

• What are five multiples of 424?

First five multiples of 424 are 848, 1272, 1696, 2120, 2544.

#### Examples of Factors

Can you help Rubel to find out the product of the even factors of 424?

Factors of 424 are 1, 2, 4, 8, 53, 106, 212, 424.
Even factors of 424 are 2, 4, 8, 106, 212, 424.
Hence, product of even factors of 424 is; 2 x 4 x 8 x 106 x 212 x 424 = 609800192.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 424? Help her in writing all the factors.

Positive factors are 1, 2, 4, 8, 53, 106, 212, 424.
Negative factors are -1, -2, -4, -8, -53, -106, -212, -424.

How many factors are there for 424?

Factors of 424 are 1, 2, 4, 8, 53, 106, 212, 424.
So there are in total 8 factors.

Sammy is puzzled while calculating the prime factors of 424. Can you help him find them?

Factors of 424 are 1, 2, 4, 8, 53, 106, 212, 424.
Prime factors of 424 are 2, 2, 2, 53

Joey wants to write all the prime factors of 424 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 424 are 2, 2, 2, 53.
So in exponential form it can be written as 23 x 53.

What is prime factorization of 424?

Prime factorization of 424 is 2 x 2 x 2 x 53 = 23 x 53.

Can you help Rubel to find out the product of the even factors of 424?

Factors of 424 are 1, 2, 4, 8, 53, 106, 212, 424.
Even factors of 424 are 2, 4, 8, 106, 212, 424.
Hence, product of even factors of 424 is; 2 x 4 x 8 x 106 x 212 x 424 = 609800192.