227 LearnersLast updated on May 26th, 2025
Factors of 490
What's your say about the factors of 490? Factors are essentially numbers that can be multiplied together to give an original number. In other words, finding those perfect pairs that go into making 490 without leaving remainders.
What are the factors of 490?
Similarly, as we learned above, factors of 490 are such numbers that will be multiplied to get 490. There are both positive and negative factors of numbers that we will learn as we move ahead in the topic.
490 has only twelve factors: 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, and 490.
Negative factors of 490: Negative factors are nothing but the negative counterparts of the position factors of a number.
Since 490 has twelve positive factors: 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, and, 490, it will also have twelve negative counterparts: -1, -2, -5, -7, -10, -14, -35, -49, -70, -98, -245, and, - 490.
Prime factors of 490: Since 490 is a composite number, it has 2, 5, and 7 as its prime factor.
Prime factorization of 490:Prime factorization of a number is the method of expressing 490 as a product of prime factors.
The prime factorization of 490 = 2× 5× 72.
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How to find the factors of 490
There are several ways of finding factors of 490. We will learn about them one by one as we go on.
Finding factors using multiplication
In this method, we will try to find such a pair of numbers that will give 490 as their product. We recommend that you should follow the following steps to find factors using multiplication.
Step 1: Always look for a pair of numbers whose product is 490.
Step 2: After finding such pairs, list them all one by one.
Here, factor pairs of 490 are (1, 490), (2, 245), (5, 98), (7, 70), (10, 49), and (14, 35).
So the factors of 490 are 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, and, 490.
Finding factors by division method
In the method, we need to find such numbers that divide 490 completely without leaving any remainder.
490/1 = 490
490/ 2 = 89
490/ 5 = 98
490/ 7 = 70
490/ 10 = 49
490/ 14 = 35
490/ 35 = 14
490/ 49 = 10
490/ 70 = 7
490/ 98 = 5
490/ 245 = 2
490/ 490 = 1
All the 12 numbers: 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, and, 490, mentioned above divide 490 completely without any remainder. Hence, they are factors of 490.
Prime Factors and Prime Factorization
In the prime factorization method, a number is expressed as the product of prime factors.
Here, as we know, 490 = 2 × 5 × 72
2, 5, and 7 are the prime factors when multiplied together will give 490 as a product of the multiplication.
Factor tree
Factor tree is a graphical representation of factors of any number. In the diagram, each branch represents the prime factors a number has.
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The factor pairs of a number refer to a pair of numbers which, when multiplied, will give the number as a product.
The factor pairs of 490 are (1, 490), (2, 245), (5, 98), (7, 70), (10, 49), and (14, 35)
Positive Pair Factors of 490 are (1, 490), (2, 245), (5, 98), (7, 70), (10, 49), and (14, 35)
Negative Pair Factors of 490 are (-1, -490), (-2, -245), (-5, -98), (-7, -70), (-10, -49), and (-14, -35)
Common Mistakes and How to Avoid Them in Factors Of 490
There are some errors that a child is bound to commit while discovering the factors of 490. Let us know what error a child is likely to commit.
Mistake 1
A child might consider only the prime factors and leave other factors.
A child must know that a number has both prime and composite factors.
Mistake 2
A child might take numbers which, when taken for division, will not give whole numbers.
A child might divide 490 with a certain number that will not give a whole number and would give a fraction. A child should remember that a number should be taken only when it can divide the original number evenly.
Mistake 3
The confusion between factors and multiples.
A child can write all multiples instead of factors. For example, the factors of 490 are 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, and, 490. But the student may instead write 980, 1470, 1960, and 2450, which are multiples of 490.
Mistake 4
A child may make some mistakes while making factorization.
A child might make some mistakes while factoring a composite number and to avoid it, a child should prefer the division method for solving.
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Factors of 490 examples
Problem 1
What is 1/ 70 of 490?
7
Explanation
You need to divide 490 by 70 to get 7.
Problem 2
What is the square root of 49.
7 is the square root of 49.
Explanation
Find the value of the square root of 49 that is 7.
Problem 3
Determine if the sum of the smallest factor of 490 and 49 is divisible by 7 or not.
No, 50 is not divisible by 7.
Explanation
The smallest factor of 490 is 1. So, 1 + 49 = 50 and 50 is not divisible by 7.
Problem 4
Calculate the number of factors of 490 by using the prime factorization method.
There are 3 prime factors of 490.
Explanation
Since 490= 72 × 2 × 5, the power of 2, 5, and 7 are 1,1 and 2. Now, add 1 to the powers and multiply. So, (1+1) * (1+1) * (2+1) = 12 factors.
Problem 5
Find the sum of all prime factors of 490 that are odd and greater than 2.
12 is the sum of all prime factors of 490.
Explanation
The prime factors greater than 2 are 5 and 7. So, the sum of 5 and 7 is 12
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FAQs on factors of 490
1.Is 490 a factor of 0?
2.Is the L.C.M. of two numbers also the factor of two numbers?
3.What is a factoring calculator used for?
4. Can 11 be a divisor of 99?
5.What is the highest power of 7 in the prime factorization of 490?
6.How can children in United Kingdom use numbers in everyday life to understand Factors of 490 ?
7.What are some fun ways kids in United Kingdom can practice Factors of 490 with numbers?
8.What role do numbers and Factors of 490 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve Factors of 490 skills?
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Important Glossaries for Factors of 490
- Prime Numbers: Those numbers which have no other factors other than 1 & the number itself.
- Composite Numbers: Those numbers that have more than 2 factors.
- Negative Factors: These are the counterparts of the positive factors of a number.
- Prime Factorization: Process of breaking down a composite number into products of several of its prime factors.
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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.
