175 LearnersLast updated on May 26th, 2025
Factors of 980
Factors of 980 are numbers that can divide 980 completely without any remainder. We often use factors for practical purposes such as organizing events and seating arrangements in our daily lives. In this topic, we will learn more about the factors of 980 and the different methods to find them.
What are the 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
How to Find the Factors of 980?
There are different methods to find the factors of 980:
Methods to find the factors of 980:
- Multiplication Method
- Division Method
- Prime Factor and Prime Factorization
- 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.
Finding Factors Using the Multiplication
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
Finding Factors Using the Division Method
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 and Prime Factorization
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
Factor Tree
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)
Common Mistakes and How to Avoid Them in Factors of 980
Mistakes can occur while finding the factors. Learn about the common errors that can occur and how to avoid them:
Mistake 1
Assuming a number like 7 is the only factor of 980.
Remember, factors are numbers that can divide the given number completely. Besides 7, 1, 2, 4, 5, 10, 14, 20, and others are also factors of 980.
Factors of 980 Examples
Problem 1
Can you check whether 980 and 1 are co-prime?
Yes, 980 and 1 are co-prime
Explanation
To check whether two numbers are co-prime, list their factors first. Once you have listed the factors, identify the common factors and determine the GCF. If the GCF is greater than 1, then the numbers are not co-prime.
Factors of 980: 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980
Factors of 1: 1 Here, the GCF is 1.
So 980 and 1 are co-prime.
Problem 2
Verify whether 980 is a multiple of 5
Yes, 980 is a multiple of 5
Explanation
Multiples of 5 are numbers we get when 5 is multiplied by another number. Since 980 ends in 0, it is divisible by 5, confirming that it is a multiple of 5.
Problem 3
Identify the perfect square from the factors of 980
The perfect square factor of 980 is 49 and the root is 7
Explanation
A perfect square is a number we get when the same number is multiplied twice. When 7 is multiplied twice (7×7), we get the perfect square 49.
Problem 4
Are the factors of 980 even or odd?
The factors of 980 include both even and odd numbers
Explanation
Factors of 980 include 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, and 980. Since 2 is one of the factors, we know there are even numbers in the list. There are also odd numbers like 1, 5, 7, 35, and 49.
FAQs on Factors of 980
1.What are the factors of 980?
2.How do you determine if a number is a factor of 980?
3.What is the smallest factor of 980?
4.What is the largest factor of 980?
5.How many factors does 980 have?
6.How many odd factors does 980 have?
7.What factors go into 980?
8.Do any perfect squares exist in the factors of 980?
Important glossaries for the Factors of 980
- 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).
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
