# Factors of 1372

Factors of 1372 are 1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686, and 1372

#### How to find factors of a number

 1.   Find factors of 1372 using Division Method 2.   Find factors of 1372 using Prime Factorization 3.   Find factors of 1372 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 1372

• Divide 1372 by 1: 1372 ÷ 1 : Remainder = 0
• Divide 1372 by 2: 1372 ÷ 2 : Remainder = 0
• Divide 1372 by 4: 1372 ÷ 4 : Remainder = 0
• Divide 1372 by 7: 1372 ÷ 7 : Remainder = 0
• Divide 1372 by 14: 1372 ÷ 14 : Remainder = 0
• Divide 1372 by 28: 1372 ÷ 28 : Remainder = 0
• Divide 1372 by 49: 1372 ÷ 49 : Remainder = 0
• Divide 1372 by 98: 1372 ÷ 98 : Remainder = 0
• Divide 1372 by 196: 1372 ÷ 196 : Remainder = 0
• Divide 1372 by 343: 1372 ÷ 343 : Remainder = 0
• Divide 1372 by 686: 1372 ÷ 686 : Remainder = 0
• Divide 1372 by 1372: 1372 ÷ 1372 : Remainder = 0

Hence, Factors of 1372 are 1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686, and 1372

#### 2. Steps to find factors of 1372 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 1372 using the division method, follow these steps:

• Step 1. Start dividing 1372 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 1372, which is 2. Divide 1372 by 2 to obtain the quotient (686).
1372 ÷ 2 = 686
• Step 3. Repeat step 1 with the obtained quotient (686).
686 ÷ 2 = 343
343 ÷ 7 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1

So, the prime factorization of 1372 is, 1372 = 2 x 2 x 7 x 7 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1372 as shown below:

So, the prime factorization of 1372 is, 1372 = 2 x 2 x 7 x 7 x 7.

#### 3. Find factors of 1372 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 1372 would be the two numbers which, when multiplied, give 1372 as the result.

The following table represents the calculation of factors of 1372 in pairs:

Factor Pair Pair Factorization
1 and 1372 1 x 1372 = 1372
2 and 686 2 x 686 = 1372
4 and 343 4 x 343 = 1372
7 and 196 7 x 196 = 1372
14 and 98 14 x 98 = 1372
28 and 49 28 x 49 = 1372

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 1372. They are called negative pair factors.

Hence, the negative pairs of 1372 would be ( -1 , -1372 ) , ( -2 , -686 ) , ( -4 , -343 ) , ( -7 , -196 ) , ( -14 , -98 ) and ( -28 , -49 ) .

#### How do you explain factors?

In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 1372 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 1372.
• Every number is a factor of zero (0), since 1372 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, 28, 49, 98, 196, 343, 686, 1372 are exact divisors of 1372.
• Factors of 1372 are 1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686, 1372. Each factor divides 1372 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686, 1372 are all less than or equal to 1372.

• Is 1372 a perfect square?

No 1372 is not a perfect square.

• What are factors of 1372?

Factors of 1372 are 1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686, 1372.

• Which is greatest factor of 1372?

The greatest factor of 1372 is 686.

• What is the sum of all factors of 1372?

The sum of all factors of 1372 is 2800.

• What are multiples of 1372?

First five multiples of 1372 are 2744, 4116, 5488, 6860.

• What is the greatest prime factors of 1372?

The greatest prime factor of 1372 is 7.

• What are six multiples of 1372?

First five multiples of 1372 are 2744, 4116, 5488, 6860, 8232, 9604.

• What is prime factorization of 1372?

Prime factorization of 1372 is 2 x 2 x 7 x 7 x 7.

• Is 1372 a whole number?

Yes 1372 is a whole number.

#### Examples of Factors

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 1372? Help her in writing all the factors.

Positive factors are 1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686, 1372.
Negative factors are -1, -2, -4, -7, -14, -28, -49, -98, -196, -343, -686, -1372.

Can you help Sammy find out the product of the odd factors of 1372?

Factors of 1372 are 1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686, 1372.
Odd factors of 1372 are 1, 7, 49, 343.
Hence product of odd factors of 1372 is; 1 x 7 x 49 x 343 = 117649.

Joey wants to write all the prime factors of 1372 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1372 are 2, 2, 7, 7, 7.
So in exponential form it can be written as 22 x 73.

How many factors are there for 1372?

Factors of 1372 are 1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686, 1372.
So there are in total 12 factors.

Kevin has been asked to write 11 factor(s) of 1372. Can you predict the answer?

11 factor(s) of 1372 are 1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686.

Sammy is puzzled while calculating the prime factors of 1372. Can you help him find them?

Factors of 1372 are 1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686, 1372.
Prime factors of 1372 are 2, 2, 7, 7, 7

What is prime factorization of 1372?

Prime factorization of 1372 is 2 x 2 x 7 x 7 x 7 = 22 x 73.