# Factors of 4900

Factors of 4900 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 49, 50, 70, 98, 100, 140, 175, 196, 245, 350, 490, 700, 980, 1225, 2450, and 4900

#### How to find factors of a number

 1.   Find factors of 4900 using Division Method 2.   Find factors of 4900 using Prime Factorization 3.   Find factors of 4900 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 4900

• Divide 4900 by 1: 4900 ÷ 1 : Remainder = 0
• Divide 4900 by 2: 4900 ÷ 2 : Remainder = 0
• Divide 4900 by 4: 4900 ÷ 4 : Remainder = 0
• Divide 4900 by 5: 4900 ÷ 5 : Remainder = 0
• Divide 4900 by 7: 4900 ÷ 7 : Remainder = 0
• Divide 4900 by 10: 4900 ÷ 10 : Remainder = 0
• Divide 4900 by 14: 4900 ÷ 14 : Remainder = 0
• Divide 4900 by 20: 4900 ÷ 20 : Remainder = 0
• Divide 4900 by 25: 4900 ÷ 25 : Remainder = 0
• Divide 4900 by 28: 4900 ÷ 28 : Remainder = 0
• Divide 4900 by 35: 4900 ÷ 35 : Remainder = 0
• Divide 4900 by 49: 4900 ÷ 49 : Remainder = 0
• Divide 4900 by 50: 4900 ÷ 50 : Remainder = 0
• Divide 4900 by 70: 4900 ÷ 70 : Remainder = 0
• Divide 4900 by 98: 4900 ÷ 98 : Remainder = 0
• Divide 4900 by 100: 4900 ÷ 100 : Remainder = 0
• Divide 4900 by 140: 4900 ÷ 140 : Remainder = 0
• Divide 4900 by 175: 4900 ÷ 175 : Remainder = 0
• Divide 4900 by 196: 4900 ÷ 196 : Remainder = 0
• Divide 4900 by 245: 4900 ÷ 245 : Remainder = 0
• Divide 4900 by 350: 4900 ÷ 350 : Remainder = 0
• Divide 4900 by 490: 4900 ÷ 490 : Remainder = 0
• Divide 4900 by 700: 4900 ÷ 700 : Remainder = 0
• Divide 4900 by 980: 4900 ÷ 980 : Remainder = 0
• Divide 4900 by 1225: 4900 ÷ 1225 : Remainder = 0
• Divide 4900 by 2450: 4900 ÷ 2450 : Remainder = 0
• Divide 4900 by 4900: 4900 ÷ 4900 : Remainder = 0

Hence, Factors of 4900 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 49, 50, 70, 98, 100, 140, 175, 196, 245, 350, 490, 700, 980, 1225, 2450, and 4900

#### 2. Steps to find factors of 4900 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 4900 using the division method, follow these steps:

• Step 1. Start dividing 4900 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 4900, which is 2. Divide 4900 by 2 to obtain the quotient (2450).
4900 ÷ 2 = 2450
• Step 3. Repeat step 1 with the obtained quotient (2450).
2450 ÷ 2 = 1225
1225 ÷ 5 = 245
245 ÷ 5 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1

So, the prime factorization of 4900 is, 4900 = 2 x 2 x 5 x 5 x 7 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 4900 as shown below:

So, the prime factorization of 4900 is, 4900 = 2 x 2 x 5 x 5 x 7 x 7.

#### 3. Find factors of 4900 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 4900 would be the two numbers which, when multiplied, give 4900 as the result.

The following table represents the calculation of factors of 4900 in pairs:

Factor Pair Pair Factorization
1 and 4900 1 x 4900 = 4900
2 and 2450 2 x 2450 = 4900
4 and 1225 4 x 1225 = 4900
5 and 980 5 x 980 = 4900
7 and 700 7 x 700 = 4900
10 and 490 10 x 490 = 4900
14 and 350 14 x 350 = 4900
20 and 245 20 x 245 = 4900
25 and 196 25 x 196 = 4900
28 and 175 28 x 175 = 4900
35 and 140 35 x 140 = 4900
49 and 100 49 x 100 = 4900
50 and 98 50 x 98 = 4900
70 and 70 70 x 70 = 4900

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 4900. They are called negative pair factors.

Hence, the negative pairs of 4900 would be ( -1 , -4900 ) , ( -2 , -2450 ) , ( -4 , -1225 ) , ( -5 , -980 ) , ( -7 , -700 ) , ( -10 , -490 ) , ( -14 , -350 ) , ( -20 , -245 ) , ( -25 , -196 ) , ( -28 , -175 ) , ( -35 , -140 ) , ( -49 , -100 ) , ( -50 , -98 ) and ( -70 , -70 ) .

#### 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. 4900 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 4900.
• Every number is a factor of zero (0), since 4900 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, 5, 7, 10, 14, 20, 25, 28, 35, 49, 50, 70, 98, 100, 140, 175, 196, 245, 350, 490, 700, 980, 1225, 2450, 4900 are exact divisors of 4900.
• Factors of 4900 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 49, 50, 70, 98, 100, 140, 175, 196, 245, 350, 490, 700, 980, 1225, 2450, 4900. Each factor divides 4900 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 49, 50, 70, 98, 100, 140, 175, 196, 245, 350, 490, 700, 980, 1225, 2450, 4900 are all less than or equal to 4900.

• Is 4900 a perfect square?

Yes 4900 is a perfect square.

• What are factors of 4900?

Factors of 4900 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 49, 50, 70, 98, 100, 140, 175, 196, 245, 350, 490, 700, 980, 1225, 2450, 4900.

• Which is greatest factor of 4900?

The greatest factor of 4900 is 2450.

• What is the sum of all factors of 4900?

The sum of all factors of 4900 is 12369.

• What are multiples of 4900?

First five multiples of 4900 are 9800, 14700, 19600, 24500.

• What is the greatest prime factors of 4900?

The greatest prime factor of 4900 is 7.

• What are six multiples of 4900?

First five multiples of 4900 are 9800, 14700, 19600, 24500, 29400, 34300.

• What is prime factorization of 4900?

Prime factorization of 4900 is 2 x 2 x 5 x 5 x 7 x 7.

• Is 4900 a whole number?

Yes 4900 is a whole number.

#### Examples of Factors

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 4900? Help her in writing all the factors.

Positive factors are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 49, 50, 70, 98, 100, 140, 175, 196, 245, 350, 490, 700, 980, 1225, 2450, 4900.
Negative factors are -1, -2, -4, -5, -7, -10, -14, -20, -25, -28, -35, -49, -50, -70, -98, -100, -140, -175, -196, -245, -350, -490, -700, -980, -1225, -2450, -4900.

Can you help Sammy find out the product of the odd factors of 4900?

Factors of 4900 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 49, 50, 70, 98, 100, 140, 175, 196, 245, 350, 490, 700, 980, 1225, 2450, 4900.
Odd factors of 4900 are 1, 5, 7, 25, 35, 49, 175, 245, 1225.
Hence product of odd factors of 4900 is; 1 x 5 x 7 x 25 x 35 x 49 x 175 x 245 x 1225 = 78815638671875.

Joey wants to write all the prime factors of 4900 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 4900 are 2, 2, 5, 5, 7, 7.
So in exponential form it can be written as 22 x 52 x 72.

How many factors are there for 4900?

Factors of 4900 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 49, 50, 70, 98, 100, 140, 175, 196, 245, 350, 490, 700, 980, 1225, 2450, 4900.
So there are in total 27 factors.

Kevin has been asked to write 26 factor(s) of 4900. Can you predict the answer?

26 factor(s) of 4900 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 49, 50, 70, 98, 100, 140, 175, 196, 245, 350, 490, 700, 980, 1225, 2450.

Sammy is puzzled while calculating the prime factors of 4900. Can you help him find them?

Factors of 4900 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 49, 50, 70, 98, 100, 140, 175, 196, 245, 350, 490, 700, 980, 1225, 2450, 4900.
Prime factors of 4900 are 2, 2, 5, 5, 7, 7

What is prime factorization of 4900?

Prime factorization of 4900 is 2 x 2 x 5 x 5 x 7 x 7 = 22 x 52 x 72.