Factors of 980

The factors of 980 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 40, 49, 70, 98, 140, 196, 245, 280, 490, and 980.

Positive Factors: These are negative counterparts of the positive factors.

Positive factors: 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 40, 49, 70, 98, 140, 196, 245, 280, 490, 980

Negative Factors: These are the negative counterparts of the positive factors.
Negative factors: -1, -2, -4, -5, -7, -10, -14, -20, -28, -35, -40, -49, -70, -98, -140, -196, -245, -280, -490, -980

Prime Factors: Prime factors are the prime numbers themselves that, when multiplied together, yield 980 as the product.
Prime factors: 2, 5, 7

Prime Factorization
Prime factorization involves breaking 980 into its prime factors and expressing it in the form of prime numbers multiplied together.
Prime Factorization: 2^2 × 5 × 7^2
 

There are different methods to find the factors of 980:

Methods to find the factors of 980:

1. Multiplication Method
2. Division Method
3. Prime Factor and Prime Factorization
4. Factor Tree

This breakdown helps in understanding the various factors of 980, whether they are positive or negative, as well as how prime factorization works for this number.
 

The multiplication method finds the pair of factors that give 980 as their product.

Step 1: Find the pair of numbers whose product is 980.
Step 2: The factors are those numbers that, when multiplied, give 980.
Step 3: Make a list of numbers whose product will be 980.

A list of numbers whose products are 980 is given below: 1 × 980 = 980

• 2 × 490 = 980
• 4 × 245 = 980
• 5 × 196 = 980
• 7 × 140 = 980
• 10 × 98 = 980
• 14 × 70 = 980
• 20 × 49 = 980
• 28 × 35 = 980
   

The division method finds the numbers that fully divide the given number. The steps are given below:

Step 1: Since every number is divisible by 1, 1 will always be a factor. Example: 980 ÷ 1 = 980.

Step 2: Move to the next integer. The factors of the number include the number that is used to divide and the quotient when the particular number is divided.
 

Prime factors of 980 can be found by dividing it by prime numbers.

Step 1: Divide 980 by 2, the smallest prime number:
980 ÷ 2 = 490

Step 2: Divide 490 by 2 again:
490 ÷ 2 = 245

Step 3: Divide 245 by 5:
245 ÷ 5 = 49

Step 4: Divide 49 by 7:
49 ÷ 7 = 7

7 ÷ 7 = 1

Prime Factorization of 980: 2² × 5 × 7²
 

The prime factorization is visually represented using the factor tree. It helps to understand the process easily.

This tree shows the breakdown of 980 into its prime factors: 2 × 2 × 5 × 7 × 7. Each branch splits into prime factors.
Factors of 980 can be written in both positive pairs and negative pairs. They are like team members whose product will equal the number given.

Positive Factor Pairs: (1, 980), (2, 490), (4, 245), (5, 196), (7, 140), (10, 98), (14, 70), (20, 49), (28, 35)

Negative Factor Pairs: (-1, -980), (-2, -490), (-4, -245), (-5, -196), (-7, -140), (-10, -98), (-14, -70), (-20, -49), (-28, -35)
 

• Factor: Numbers that can divide 980 completely without leaving any remainder.

• Prime Factors: The prime numbers themselves that, when multiplied together, yield 980 as the product (e.g., 2, 5, 7).

• Prime Factorization: Breaking down 980 into its prime factors expressed as prime numbers multiplied together (e.g., 2²×5×7²).

• Perfect Square: A number we get when the same number is multiplied twice (e.g., 49, since 7×7=49).

• Multiple: Numbers we get when another number multiplies the given number (e.g., 980 is a multiple of 5, as 5×196=980).