# Factors of 476

Factors of 476 are 1, 2, 4, 7, 14, 17, 28, 34, 68, 119, 238, and 476

#### How to find factors of a number

 1.   Find factors of 476 using Division Method 2.   Find factors of 476 using Prime Factorization 3.   Find factors of 476 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 476

• Divide 476 by 1: 476 ÷ 1 : Remainder = 0
• Divide 476 by 2: 476 ÷ 2 : Remainder = 0
• Divide 476 by 4: 476 ÷ 4 : Remainder = 0
• Divide 476 by 7: 476 ÷ 7 : Remainder = 0
• Divide 476 by 14: 476 ÷ 14 : Remainder = 0
• Divide 476 by 17: 476 ÷ 17 : Remainder = 0
• Divide 476 by 28: 476 ÷ 28 : Remainder = 0
• Divide 476 by 34: 476 ÷ 34 : Remainder = 0
• Divide 476 by 68: 476 ÷ 68 : Remainder = 0
• Divide 476 by 119: 476 ÷ 119 : Remainder = 0
• Divide 476 by 238: 476 ÷ 238 : Remainder = 0
• Divide 476 by 476: 476 ÷ 476 : Remainder = 0

Hence, Factors of 476 are 1, 2, 4, 7, 14, 17, 28, 34, 68, 119, 238, and 476

#### 2. Steps to find factors of 476 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 476 using the division method, follow these steps:

• Step 1. Start dividing 476 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 476, which is 2. Divide 476 by 2 to obtain the quotient (238).
476 ÷ 2 = 238
• Step 3. Repeat step 1 with the obtained quotient (238).
238 ÷ 2 = 119
119 ÷ 7 = 17
17 ÷ 17 = 1

So, the prime factorization of 476 is, 476 = 2 x 2 x 7 x 17.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 476 as shown below:

So, the prime factorization of 476 is, 476 = 2 x 2 x 7 x 17.

#### 3. Find factors of 476 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 476 would be the two numbers which, when multiplied, give 476 as the result.

The following table represents the calculation of factors of 476 in pairs:

Factor Pair Pair Factorization
1 and 476 1 x 476 = 476
2 and 238 2 x 238 = 476
4 and 119 4 x 119 = 476
7 and 68 7 x 68 = 476
14 and 34 14 x 34 = 476
17 and 28 17 x 28 = 476

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 476. They are called negative pair factors.

Hence, the negative pairs of 476 would be ( -1 , -476 ) , ( -2 , -238 ) , ( -4 , -119 ) , ( -7 , -68 ) , ( -14 , -34 ) and ( -17 , -28 ) .

#### 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. 476 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 476.
• Every number is a factor of zero (0), since 476 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, 14, 17, 28, 34, 68, 119, 238, 476 are exact divisors of 476.
• Factors of 476 are 1, 2, 4, 7, 14, 17, 28, 34, 68, 119, 238, 476. Each factor divides 476 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 7, 14, 17, 28, 34, 68, 119, 238, 476 are all less than or equal to 476.

• What is prime factorization of 476?

Prime factorization of 476 is 2 x 2 x 7 x 17.

• How do you find factors of a negative number? ( eg. -476 )?

Factors of -476 are -1, -2, -4, -7, -14, -17, -28, -34, -68, -119, -238, -476.

• What are the prime factors of 476?

The factors of 476 are 1, 2, 4, 7, 14, 17, 28, 34, 68, 119, 238, 476.
Prime factors of 476 are 2, 2, 7, 17.

• What are pair factors of 476?

The pair factors of 476 are (1,476), (2,238), (4,119), (7,68), (14,34), (17,28).

• What is the greatest prime factors of 476?

The greatest prime factor of 476 is 17.

• What are six multiples of 476?

First five multiples of 476 are 952, 1428, 1904, 2380, 2856, 3332.

• What are factors of 476?

Factors of 476 are 1, 2, 4, 7, 14, 17, 28, 34, 68, 119, 238, 476.

• Which is the smallest prime factor of 476?

Smallest prime factor of 476 is 2.

• Is 476 a whole number?

Yes 476 is a whole number.

#### Examples of Factors

Kevin has been asked to write 11 factor(s) of 476. Can you predict the answer?

11 factor(s) of 476 are 1, 2, 4, 7, 14, 17, 28, 34, 68, 119, 238.

Sammy is puzzled while calculating the prime factors of 476. Can you help him find them?

Factors of 476 are 1, 2, 4, 7, 14, 17, 28, 34, 68, 119, 238, 476.
Prime factors of 476 are 2, 2, 7, 17

What is prime factorization of 476?

Prime factorization of 476 is 2 x 2 x 7 x 17 = 22 x 7 x 17.

Ariel has been assigned the task to find the product of all the prime factors of 476. Can you help her?

Prime factors of 476 are 2, 2, 7, 17.
Hence, the product of prime factors of 238.

Can you help Rubel to find out the product of the even factors of 476?

Factors of 476 are 1, 2, 4, 7, 14, 17, 28, 34, 68, 119, 238, 476.
Even factors of 476 are 2, 4, 14, 28, 34, 68, 238, 476.
Hence, product of even factors of 476 is; 2 x 4 x 14 x 28 x 34 x 68 x 238 x 476 = 821386940416.

Joy wants to calculate mean of all the factors of 476. Help him in finding the mean of 476.

Factors of 476 are 1, 2, 4, 7, 14, 17, 28, 34, 68, 119, 238, 476.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 476 is 1 + 2 + 4 + 7 + 14 + 17 + 28 + 34 + 68 + 119 + 238 + 476 = 1008.
Hence, the mean of factors of 476 is 1008 ÷ 12 = 84.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 476? Help her in writing all the factors.

Positive factors are 1, 2, 4, 7, 14, 17, 28, 34, 68, 119, 238, 476.
Negative factors are -1, -2, -4, -7, -14, -17, -28, -34, -68, -119, -238, -476.