# Factors of 77

Factors of 77 are 1, 7, 11, and 77

#### How to find factors of a number

 1.   Find factors of 77 using Division Method 2.   Find factors of 77 using Prime Factorization 3.   Find factors of 77 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 77

• Divide 77 by 1: 77 ÷ 1 : Remainder = 0
• Divide 77 by 7: 77 ÷ 7 : Remainder = 0
• Divide 77 by 11: 77 ÷ 11 : Remainder = 0
• Divide 77 by 77: 77 ÷ 77 : Remainder = 0

Hence, Factors of 77 are 1, 7, 11, and 77

#### 2. Steps to find factors of 77 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 77 using the division method, follow these steps:

• Step 1. Start dividing 77 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 77, which is 7. Divide 77 by 7 to obtain the quotient (11).
77 ÷ 7 = 11
• Step 3. Repeat step 1 with the obtained quotient (11).
11 ÷ 11 = 1

So, the prime factorization of 77 is, 77 = 7 x 11.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 77 as shown below:

So, the prime factorization of 77 is, 77 = 7 x 11.

#### 3. Find factors of 77 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 77 would be the two numbers which, when multiplied, give 77 as the result.

The following table represents the calculation of factors of 77 in pairs:

Factor Pair Pair Factorization
1 and 77 1 x 77 = 77
7 and 11 7 x 11 = 77

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 77. They are called negative pair factors.

Hence, the negative pairs of 77 would be ( -1 , -77 ) , ( -7 , -11 ) .

#### 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

• Every factor of a number is an exact divisor of that number, example 1, 7, 11, 77 are exact divisors of 77.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 77 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 77.

• What are the pair factors of 77?

Pair factors of 77 are (1,77), (7,11).

• What are five multiples of 77?

First five multiples of 77 are 154, 231, 308, 385, 462.

• What two numbers make 77?

Two numbers that make 77 are 7 and 11.

• What is the sum of all factors of 77?

The sum of all factors of 77 is 96.

• What are factors of -77?

Factors of -77 are -1, -7, -11, -77.

• What are factors of 77?

Factors of 77 are 1, 7, 11, 77.

• Is 77 a perfect square?

No 77 is not a perfect square.

• Which is the smallest prime factor of 77?

Smallest prime factor of 77 is 7.

• Which is greatest factor of 77?

The greatest factor of 77 is 11.

#### Examples of Factors

Can you help Sammy find out the product of the odd factors of 77?

Factors of 77 are 1, 7, 11, 77.
Odd factors of 77 are 1, 7, 11, 77.
Hence product of odd factors of 77 is; 1 x 7 x 11 x 77 = 5929.

Joey wants to write all the prime factors of 77 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 77 are 7, 11.
So in exponential form it can be written as 7 x 11.

How many factors are there for 77?

Factors of 77 are 1, 7, 11, 77.
So there are in total 4 factors.

Kevin has been asked to write 3 factor(s) of 77. Can you predict the answer?

3 factor(s) of 77 are 1, 7, 11.

Sammy is puzzled while calculating the prime factors of 77. Can you help him find them?

Factors of 77 are 1, 7, 11, 77.
Prime factors of 77 are 7, 11

What is prime factorization of 77?

Prime factorization of 77 is 7 x 11 = 7 x 11.

Can you help Rubel to find out the product of the even factors of 77?

Factors of 77 are 1, 7, 11, 77.
Even factors of 77 are 0.
Hence, product of even factors of 77 is; 0 = 0.