# Factors of 350

Factors of 350 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, and 350

#### How to find factors of a number

 1.   Find factors of 350 using Division Method 2.   Find factors of 350 using Prime Factorization 3.   Find factors of 350 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 350

• Divide 350 by 1: 350 ÷ 1 : Remainder = 0
• Divide 350 by 2: 350 ÷ 2 : Remainder = 0
• Divide 350 by 5: 350 ÷ 5 : Remainder = 0
• Divide 350 by 7: 350 ÷ 7 : Remainder = 0
• Divide 350 by 10: 350 ÷ 10 : Remainder = 0
• Divide 350 by 14: 350 ÷ 14 : Remainder = 0
• Divide 350 by 25: 350 ÷ 25 : Remainder = 0
• Divide 350 by 35: 350 ÷ 35 : Remainder = 0
• Divide 350 by 50: 350 ÷ 50 : Remainder = 0
• Divide 350 by 70: 350 ÷ 70 : Remainder = 0
• Divide 350 by 175: 350 ÷ 175 : Remainder = 0
• Divide 350 by 350: 350 ÷ 350 : Remainder = 0

Hence, Factors of 350 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, and 350

#### 2. Steps to find factors of 350 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 350 using the division method, follow these steps:

• Step 1. Start dividing 350 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 350, which is 2. Divide 350 by 2 to obtain the quotient (175).
350 ÷ 2 = 175
• Step 3. Repeat step 1 with the obtained quotient (175).
175 ÷ 5 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1

So, the prime factorization of 350 is, 350 = 2 x 5 x 5 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 350 as shown below:

So, the prime factorization of 350 is, 350 = 2 x 5 x 5 x 7.

#### 3. Find factors of 350 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 350 would be the two numbers which, when multiplied, give 350 as the result.

The following table represents the calculation of factors of 350 in pairs:

Factor Pair Pair Factorization
1 and 350 1 x 350 = 350
2 and 175 2 x 175 = 350
5 and 70 5 x 70 = 350
7 and 50 7 x 50 = 350
10 and 35 10 x 35 = 350
14 and 25 14 x 25 = 350

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 350. They are called negative pair factors.

Hence, the negative pairs of 350 would be ( -1 , -350 ) , ( -2 , -175 ) , ( -5 , -70 ) , ( -7 , -50 ) , ( -10 , -35 ) and ( -14 , -25 ) .

#### 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. 350 is a factor of itself.
• 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, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350 are exact divisors of 350.
• 1 is a factor of every number. Eg. 1 is a factor of 350.
• Every number is a factor of zero (0), since 350 x 0 = 0.

• What is prime factorization of 350?

Prime factorization of 350 is 2 x 5 x 5 x 7.

• How do you find factors of a negative number? ( eg. -350 )?

Factors of -350 are -1, -2, -5, -7, -10, -14, -25, -35, -50, -70, -175, -350.

• What are the prime factors of 350?

The factors of 350 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350.
Prime factors of 350 are 2, 5, 5, 7.

• What are pair factors of 350?

The pair factors of 350 are (1,350), (2,175), (5,70), (7,50), (10,35), (14,25).

• What is the greatest prime factors of 350?

The greatest prime factor of 350 is 7.

• What are six multiples of 350?

First five multiples of 350 are 700, 1050, 1400, 1750, 2100, 2450.

• What are factors of 350?

Factors of 350 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350.

• Which is the smallest prime factor of 350?

Smallest prime factor of 350 is 2.

• Is 350 a whole number?

Yes 350 is a whole number.

#### Examples of Factors

Kevin has been asked to write 11 factor(s) of 350. Can you predict the answer?

11 factor(s) of 350 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175.

Sammy is puzzled while calculating the prime factors of 350. Can you help him find them?

Factors of 350 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350.
Prime factors of 350 are 2, 5, 5, 7

What is prime factorization of 350?

Prime factorization of 350 is 2 x 5 x 5 x 7 = 2 x 52 x 7.

Ariel has been assigned the task to find the product of all the prime factors of 350. Can you help her?

Prime factors of 350 are 2, 5, 5, 7.
Hence, the product of prime factors of 70.

Can you help Rubel to find out the product of the even factors of 350?

Factors of 350 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350.
Even factors of 350 are 2, 10, 14, 50, 70, 350.
Hence, product of even factors of 350 is; 2 x 10 x 14 x 50 x 70 x 350 = 343000000.

Joy wants to calculate mean of all the factors of 350. Help him in finding the mean of 350.

Factors of 350 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 350 is 1 + 2 + 5 + 7 + 10 + 14 + 25 + 35 + 50 + 70 + 175 + 350 = 744.
Hence, the mean of factors of 350 is 744 ÷ 12 = 62.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 350? Help her in writing all the factors.

Positive factors are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350.
Negative factors are -1, -2, -5, -7, -10, -14, -25, -35, -50, -70, -175, -350.