# Factors of 1750

Factors of 1750 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 125, 175, 250, 350, 875, and 1750

#### How to find factors of a number

 1.   Find factors of 1750 using Division Method 2.   Find factors of 1750 using Prime Factorization 3.   Find factors of 1750 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 1750

• Divide 1750 by 1: 1750 ÷ 1 : Remainder = 0
• Divide 1750 by 2: 1750 ÷ 2 : Remainder = 0
• Divide 1750 by 5: 1750 ÷ 5 : Remainder = 0
• Divide 1750 by 7: 1750 ÷ 7 : Remainder = 0
• Divide 1750 by 10: 1750 ÷ 10 : Remainder = 0
• Divide 1750 by 14: 1750 ÷ 14 : Remainder = 0
• Divide 1750 by 25: 1750 ÷ 25 : Remainder = 0
• Divide 1750 by 35: 1750 ÷ 35 : Remainder = 0
• Divide 1750 by 50: 1750 ÷ 50 : Remainder = 0
• Divide 1750 by 70: 1750 ÷ 70 : Remainder = 0
• Divide 1750 by 125: 1750 ÷ 125 : Remainder = 0
• Divide 1750 by 175: 1750 ÷ 175 : Remainder = 0
• Divide 1750 by 250: 1750 ÷ 250 : Remainder = 0
• Divide 1750 by 350: 1750 ÷ 350 : Remainder = 0
• Divide 1750 by 875: 1750 ÷ 875 : Remainder = 0
• Divide 1750 by 1750: 1750 ÷ 1750 : Remainder = 0

Hence, Factors of 1750 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 125, 175, 250, 350, 875, and 1750

#### 2. Steps to find factors of 1750 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 1750 using the division method, follow these steps:

• Step 1. Start dividing 1750 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 1750, which is 2. Divide 1750 by 2 to obtain the quotient (875).
1750 ÷ 2 = 875
• Step 3. Repeat step 1 with the obtained quotient (875).
875 ÷ 5 = 175
175 ÷ 5 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1

So, the prime factorization of 1750 is, 1750 = 2 x 5 x 5 x 5 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1750 as shown below:

So, the prime factorization of 1750 is, 1750 = 2 x 5 x 5 x 5 x 7.

#### 3. Find factors of 1750 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 1750 would be the two numbers which, when multiplied, give 1750 as the result.

The following table represents the calculation of factors of 1750 in pairs:

Factor Pair Pair Factorization
1 and 1750 1 x 1750 = 1750
2 and 875 2 x 875 = 1750
5 and 350 5 x 350 = 1750
7 and 250 7 x 250 = 1750
10 and 175 10 x 175 = 1750
14 and 125 14 x 125 = 1750
25 and 70 25 x 70 = 1750
35 and 50 35 x 50 = 1750

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 1750. They are called negative pair factors.

Hence, the negative pairs of 1750 would be ( -1 , -1750 ) , ( -2 , -875 ) , ( -5 , -350 ) , ( -7 , -250 ) , ( -10 , -175 ) , ( -14 , -125 ) , ( -25 , -70 ) and ( -35 , -50 ) .

#### 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. 1750 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, 125, 175, 250, 350, 875, 1750 are exact divisors of 1750.
• 1 is a factor of every number. Eg. 1 is a factor of 1750.
• Every number is a factor of zero (0), since 1750 x 0 = 0.

• Is 1750 a perfect square?

No 1750 is not a perfect square.

• What are factors of 1750?

Factors of 1750 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 125, 175, 250, 350, 875, 1750.

• Which is greatest factor of 1750?

The greatest factor of 1750 is 875.

• What is the sum of all factors of 1750?

The sum of all factors of 1750 is 3744.

• What are multiples of 1750?

First five multiples of 1750 are 3500, 5250, 7000, 8750.

• What is the greatest prime factors of 1750?

The greatest prime factor of 1750 is 7.

• What are six multiples of 1750?

First five multiples of 1750 are 3500, 5250, 7000, 8750, 10500, 12250.

• What is prime factorization of 1750?

Prime factorization of 1750 is 2 x 5 x 5 x 5 x 7.

• Is 1750 a whole number?

Yes 1750 is a whole number.

#### Examples of Factors

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 1750? Help her in writing all the factors.

Positive factors are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 125, 175, 250, 350, 875, 1750.
Negative factors are -1, -2, -5, -7, -10, -14, -25, -35, -50, -70, -125, -175, -250, -350, -875, -1750.

Can you help Sammy find out the product of the odd factors of 1750?

Factors of 1750 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 125, 175, 250, 350, 875, 1750.
Odd factors of 1750 are 1, 5, 7, 25, 35, 125, 175, 875.
Hence product of odd factors of 1750 is; 1 x 5 x 7 x 25 x 35 x 125 x 175 x 875 = 586181640625.

Joey wants to write all the prime factors of 1750 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1750 are 2, 5, 5, 5, 7.
So in exponential form it can be written as 2 x 53 x 7.

How many factors are there for 1750?

Factors of 1750 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 125, 175, 250, 350, 875, 1750.
So there are in total 16 factors.

Kevin has been asked to write 15 factor(s) of 1750. Can you predict the answer?

15 factor(s) of 1750 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 125, 175, 250, 350, 875.

Sammy is puzzled while calculating the prime factors of 1750. Can you help him find them?

Factors of 1750 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 125, 175, 250, 350, 875, 1750.
Prime factors of 1750 are 2, 5, 5, 5, 7

What is prime factorization of 1750?

Prime factorization of 1750 is 2 x 5 x 5 x 5 x 7 = 2 x 53 x 7.