217 LearnersLast updated on May 26th, 2025
Factors of 1225
What's your say about the factors of 1225? 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 1225 without leaving remainders.
What are the Factors of 1225?
Similarly, as we learned above, factors of 1225 are such numbers that will be multiplied to get 1225. There are both positive and negative factors of numbers that we will learn as we move ahead in the topic.
1225 has only 9 factors: 1, 5, 7, 25, 35, 49, 175, 245 and 1225.
Negative factors of 1225: Negative factors are nothing but the negative counterparts of the position factors of a number.
Since 1225 has 9 positive factors: 1, 5, 7, 25, 35, 49, 175, 245, and 1225, it will also have 9 negative counterparts, which are -1, -5, -7, -25, -35, -49, -175, -245 and -1225.
Prime factors of 1225: Since 1225 is a composite number, it will have 5 and 7 as its prime factors.
Prime factorization of 1225: Prime factorization of a number is the method of expressing 1225 as a product of prime factors.
The prime factorization of 1225 = 5 Ñ… 5 Ñ… 7 Ñ… 7.
How to find the factors of 1225
There are several ways of finding factors of 1225. 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 1225 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 1225.
Step 2: After finding such pairs, list them all one by one.
Here, factor pairs of 1225 are (1, 1225), (5, 84), (7, 175), (25, 49), (35, 35)
So the factors of 1225 are 1, 5, 7, 25, 35, 49, 175, 245, and 1225.
Finding factors by division method
In the method, we need to find such numbers that divide 1225 completely without leaving any remainder.
1225/1 = 1225
1225/ 5 = 245
1225/ 7 = 175
1225/ 25 = 49
1225/ 35 = 35
1225/ 49 = 25
1225/ 175 = 7
1225 / 245 = 5
1225/ 1225 = 1
All the 9 numbers: 1, 5, 7, 25, 35, 49, 175, 245, and 1225 mentioned above divide 1225 completely without any remainder. Hence, they are factors of 1225.
Prime Factors and Prime Factorization
In the prime factorization method, a number is expressed as the product of prime factors.
Here, as we know, 1225 = 5Ñ… 5 Ñ… 7Ñ… 7
52 and 72 are the prime factors whose multiplication will give 1225 as a product of prime numbers.
Factor tree
A factor tree is a graphical representation of factors of any number. In the diagram, each branch represents the prime factors a number has.
Factor Pairs
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 1225 are (1, 1225), (5, 84), (7, 175), (25, 49), (35, 35).
Positive Pair Factors of 1225 are (1, 1225), (5, 84), (7, 175), (25, 49), (35, 35)
Negative Pair Factors of 1225 are (-1, -1225), (-5, -84), (-7, -175), (-25, -49), (-35, -35)
Common Mistakes and How to Avoid Them in Factors of 1225
There are some errors which a child is bound to commit while discovering the factors of 1225. Let us know what error a child is likely to commit.
Mistake 1
A child might leave certain prime factors while calculating.
A child must take into consideration all the factors that a number has, and should not only take prime numbers or only composite numbers.
Factors of 1225 examples
Problem 1
What are the prime numbers that shall be multiplied with 1225 to make it a perfect cube?
5 and 7 are the prime numbers that should be multiplied with 1225.
Explanation
When 1225 is multiplied with 1225 with 5 × 7 = 35, i.e., 1225 × 35 =42875. Cube root of 42875 is 35.
Problem 2
If the ratio of two factors of 1225 is 7 : 5, then find the factors.
49 and 35 are the two factors of 1225 whose ratio is 7 : 5.
Explanation
The factors of 1225 are 1, 5, 7, 25, 35, 49, 175, 245, and 1225 and out of those, if we simplify 49 / 35, then we get 7/5 or 7:5.
Problem 3
Prove that 25 and 49 are the factors of 1225.
Prime factorization of 1225 is 5 × 5 × 7 × 7. Here, 5 × 5 = 25 and 7 × 7 = 49.
Explanation
So, 25 and 49 are the factors of 1225.
Problem 4
So, 25 and 49 are the factors of 1225.
11,025 is the smallest multiple of 1225 that is greater than 10,000.
Explanation
We will know how to solve this question through steps.
Step 1 : Divide 10,000 by 1225 to get 8.163.
Step 2 : We know that to be greater than 10,000, we need to multiply 1225 with a number greater than 8.163. So, let's take 9 and 1225 × 9 = 11025.
Step 3 : Hence, 11,025 is the smallest multiple of 1225 that is greater than 10,000.
Problem 5
List two factors of 1225 which divides 1225 without leaving any remainder.
25 and 49 are the two factors of 1225 which when divided by 1225 does not leave any remainder.
Explanation
1225 when divided by 25 and 49, gets divided completely without leaving behind any remainder. Hence, 25 and 49 are two factors of 1225 which divides 1225 without leaving any remainder.
FAQs on Factors of 1225
1.How many factors of 1225 are there?
2.Is 69 a perfect square?
3.Is 1225 divisible by 15?
4.Can you tell if fractions are rational or irrational numbers ?
5.Can you tell if 1225 is divisible by 3?
Important Glossaries for Factors of 1225
- 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.
