# Factors of 980

Factors of 980 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, and 980

#### How to find factors of a number

 1.   Find factors of 980 using Division Method 2.   Find factors of 980 using Prime Factorization 3.   Find factors of 980 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 980

• Divide 980 by 1: 980 ÷ 1 : Remainder = 0
• Divide 980 by 2: 980 ÷ 2 : Remainder = 0
• Divide 980 by 4: 980 ÷ 4 : Remainder = 0
• Divide 980 by 5: 980 ÷ 5 : Remainder = 0
• Divide 980 by 7: 980 ÷ 7 : Remainder = 0
• Divide 980 by 10: 980 ÷ 10 : Remainder = 0
• Divide 980 by 14: 980 ÷ 14 : Remainder = 0
• Divide 980 by 20: 980 ÷ 20 : Remainder = 0
• Divide 980 by 28: 980 ÷ 28 : Remainder = 0
• Divide 980 by 35: 980 ÷ 35 : Remainder = 0
• Divide 980 by 49: 980 ÷ 49 : Remainder = 0
• Divide 980 by 70: 980 ÷ 70 : Remainder = 0
• Divide 980 by 98: 980 ÷ 98 : Remainder = 0
• Divide 980 by 140: 980 ÷ 140 : Remainder = 0
• Divide 980 by 196: 980 ÷ 196 : Remainder = 0
• Divide 980 by 245: 980 ÷ 245 : Remainder = 0
• Divide 980 by 490: 980 ÷ 490 : Remainder = 0
• Divide 980 by 980: 980 ÷ 980 : Remainder = 0

Hence, Factors of 980 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, and 980

#### 2. Steps to find factors of 980 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 980 using the division method, follow these steps:

• Step 1. Start dividing 980 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 980, which is 2. Divide 980 by 2 to obtain the quotient (490).
980 ÷ 2 = 490
• Step 3. Repeat step 1 with the obtained quotient (490).
490 ÷ 2 = 245
245 ÷ 5 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1

So, the prime factorization of 980 is, 980 = 2 x 2 x 5 x 7 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 980 as shown below:

So, the prime factorization of 980 is, 980 = 2 x 2 x 5 x 7 x 7.

#### 3. Find factors of 980 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 980 would be the two numbers which, when multiplied, give 980 as the result.

The following table represents the calculation of factors of 980 in pairs:

Factor Pair Pair Factorization
1 and 980 1 x 980 = 980
2 and 490 2 x 490 = 980
4 and 245 4 x 245 = 980
5 and 196 5 x 196 = 980
7 and 140 7 x 140 = 980
10 and 98 10 x 98 = 980
14 and 70 14 x 70 = 980
20 and 49 20 x 49 = 980
28 and 35 28 x 35 = 980

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 980. They are called negative pair factors.

Hence, the negative pairs of 980 would be ( -1 , -980 ) , ( -2 , -490 ) , ( -4 , -245 ) , ( -5 , -196 ) , ( -7 , -140 ) , ( -10 , -98 ) , ( -14 , -70 ) , ( -20 , -49 ) and ( -28 , -35 ) .

#### 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. 980 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 980.
• Every number is a factor of zero (0), since 980 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, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980 are exact divisors of 980.
• Factors of 980 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980. Each factor divides 980 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, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980 are all less than or equal to 980.

• What is prime factorization of 980?

Prime factorization of 980 is 2 x 2 x 5 x 7 x 7.

• How do you find factors of a negative number? ( eg. -980 )?

Factors of -980 are -1, -2, -4, -5, -7, -10, -14, -20, -28, -35, -49, -70, -98, -140, -196, -245, -490, -980.

• What are the prime factors of 980?

The factors of 980 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980.
Prime factors of 980 are 2, 2, 5, 7, 7.

• What are pair factors of 980?

The pair factors of 980 are (1,980), (2,490), (4,245), (5,196), (7,140), (10,98), (14,70), (20,49), (28,35).

• What is the greatest prime factors of 980?

The greatest prime factor of 980 is 7.

• What are six multiples of 980?

First five multiples of 980 are 1960, 2940, 3920, 4900, 5880, 6860.

• What are factors of 980?

Factors of 980 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980.

• Which is the smallest prime factor of 980?

Smallest prime factor of 980 is 2.

• Is 980 a whole number?

Yes 980 is a whole number.

#### Examples of Factors

Kevin has been asked to write 17 factor(s) of 980. Can you predict the answer?

17 factor(s) of 980 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490.

Sammy is puzzled while calculating the prime factors of 980. Can you help him find them?

Factors of 980 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980.
Prime factors of 980 are 2, 2, 5, 7, 7

What is prime factorization of 980?

Prime factorization of 980 is 2 x 2 x 5 x 7 x 7 = 22 x 5 x 72.

Ariel has been assigned the task to find the product of all the prime factors of 980. Can you help her?

Prime factors of 980 are 2, 2, 5, 7, 7.
Hence, the product of prime factors of 70.

Can you help Rubel to find out the product of the even factors of 980?

Factors of 980 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980.
Even factors of 980 are 2, 4, 10, 14, 20, 28, 70, 98, 140, 196, 490, 980.
Hence, product of even factors of 980 is; 2 x 4 x 10 x 14 x 20 x 28 x 70 x 98 x 140 x 196 x 490 x 980 = 56693912375296000000.

Joy wants to calculate mean of all the factors of 980. Help him in finding the mean of 980.

Factors of 980 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 980 is 1 + 2 + 4 + 5 + 7 + 10 + 14 + 20 + 28 + 35 + 49 + 70 + 98 + 140 + 196 + 245 + 490 + 980 = 2394.
Hence, the mean of factors of 980 is 2394 ÷ 18 = 133.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 980? Help her in writing all the factors.

Positive factors are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980.
Negative factors are -1, -2, -4, -5, -7, -10, -14, -20, -28, -35, -49, -70, -98, -140, -196, -245, -490, -980.