# Factors of 712

Factors of 712 are 1, 2, 4, 8, 89, 178, 356, and 712

#### How to find factors of a number

 1.   Find factors of 712 using Division Method 2.   Find factors of 712 using Prime Factorization 3.   Find factors of 712 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 712

• Divide 712 by 1: 712 ÷ 1 : Remainder = 0
• Divide 712 by 2: 712 ÷ 2 : Remainder = 0
• Divide 712 by 4: 712 ÷ 4 : Remainder = 0
• Divide 712 by 8: 712 ÷ 8 : Remainder = 0
• Divide 712 by 89: 712 ÷ 89 : Remainder = 0
• Divide 712 by 178: 712 ÷ 178 : Remainder = 0
• Divide 712 by 356: 712 ÷ 356 : Remainder = 0
• Divide 712 by 712: 712 ÷ 712 : Remainder = 0

Hence, Factors of 712 are 1, 2, 4, 8, 89, 178, 356, and 712

#### 2. Steps to find factors of 712 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 712 using the division method, follow these steps:

• Step 1. Start dividing 712 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 712, which is 2. Divide 712 by 2 to obtain the quotient (356).
712 ÷ 2 = 356
• Step 3. Repeat step 1 with the obtained quotient (356).
356 ÷ 2 = 178
178 ÷ 2 = 89
89 ÷ 89 = 1

So, the prime factorization of 712 is, 712 = 2 x 2 x 2 x 89.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 712 as shown below:

So, the prime factorization of 712 is, 712 = 2 x 2 x 2 x 89.

#### 3. Find factors of 712 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 712 would be the two numbers which, when multiplied, give 712 as the result.

The following table represents the calculation of factors of 712 in pairs:

Factor Pair Pair Factorization
1 and 712 1 x 712 = 712
2 and 356 2 x 356 = 712
4 and 178 4 x 178 = 712
8 and 89 8 x 89 = 712

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 712. They are called negative pair factors.

Hence, the negative pairs of 712 would be ( -1 , -712 ) , ( -2 , -356 ) , ( -4 , -178 ) and ( -8 , -89 ) .

#### 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. 712 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 712.
• Every number is a factor of zero (0), since 712 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, 89, 178, 356, 712 are exact divisors of 712.
• Factors of 712 are 1, 2, 4, 8, 89, 178, 356, 712. Each factor divides 712 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 8, 89, 178, 356, 712 are all less than or equal to 712.

• What are the prime factors of 712?

The factors of 712 are 1, 2, 4, 8, 89, 178, 356, 712.
Prime factors of 712 are 2, 2, 2, 89.

• What is the sum of all factors of 712?

The sum of all factors of 712 is 1350.

• What are the pair factors of 712?

Pair factors of 712 are (1,712), (2,356), (4,178), (8,89).

• What two numbers make 712?

Two numbers that make 712 are 2 and 356.

• What are multiples of 712?

First five multiples of 712 are 1424, 2136, 2848, 3560.

• Is 712 a perfect square?

No 712 is not a perfect square.

• Which is greatest factor of 712?

The greatest factor of 712 is 356.

• How do you factors of 712?

Factors of 712 are 1, 2, 4, 8, 89, 178, 356, 712.

• What are five multiples of 712?

First five multiples of 712 are 1424, 2136, 2848, 3560, 4272.

#### Examples of Factors

Can you help Rubel to find out the product of the even factors of 712?

Factors of 712 are 1, 2, 4, 8, 89, 178, 356, 712.
Even factors of 712 are 2, 4, 8, 178, 356, 712.
Hence, product of even factors of 712 is; 2 x 4 x 8 x 178 x 356 x 712 = 2887553024.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 712? Help her in writing all the factors.

Positive factors are 1, 2, 4, 8, 89, 178, 356, 712.
Negative factors are -1, -2, -4, -8, -89, -178, -356, -712.

How many factors are there for 712?

Factors of 712 are 1, 2, 4, 8, 89, 178, 356, 712.
So there are in total 8 factors.

Sammy is puzzled while calculating the prime factors of 712. Can you help him find them?

Factors of 712 are 1, 2, 4, 8, 89, 178, 356, 712.
Prime factors of 712 are 2, 2, 2, 89

Joey wants to write all the prime factors of 712 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 712 are 2, 2, 2, 89.
So in exponential form it can be written as 23 x 89.

What is prime factorization of 712?

Prime factorization of 712 is 2 x 2 x 2 x 89 = 23 x 89.

Can you help Rubel to find out the product of the even factors of 712?

Factors of 712 are 1, 2, 4, 8, 89, 178, 356, 712.
Even factors of 712 are 2, 4, 8, 178, 356, 712.
Hence, product of even factors of 712 is; 2 x 4 x 8 x 178 x 356 x 712 = 2887553024.