152 LearnersLast updated on May 26th, 2025
Factors of 413
Factors are the ‘building blocks’ of a number. They are the numbers that can be multiplied together to reach the number you started with. 413 is an interesting number. It is large enough to make you think, but simple enough to learn if you know a few tricks. Let’s dive into it!
What are the factors of 413?
Factors are whole numbers that, when multiplied, the product is equal to 413.
413 is not a prime number, its factors are 1,7,59,413. For every factor, there is a corresponding negative factor, for 413, the negative factors -1,-7,-59,-413.
How to find the factors of 413?
There are various methods we apply to find the factors of any number. Few of them are listed here; multiplication method, division method, prime factors and prime factorization and factor tree method. These are explained in detail below, let’s learn !
Finding Factors Using Multiplication
Step 1: Find all pairs of numbers whose product is 413.
Step 2: All the pairs found represent the factors of 413.
413 is not a prime number. The pair of numbers whose product is 413 is;
1×413=413
7×59 = 413
The factors of 413 are 1,7,59,413.
Finding Factors by Division Method
Step 1: Start by dividing 413 with the smallest number, and check the remainders.
Step 2: 413 is not prime, therefore the divisors it has are 1,7,59,413. Any number that is further checked for divisibility leaves behind a remainder.
The factors of 413 are 1,7,59,413.
Prime factors and prime factorization
— 413 is not a prime number.
— The prime factorization of 413 is 7×59.
— Factors of 413 are 1,7,59,413.
Factor tree
— In this method, we make branches that extend from the number to express a number as the product of its factors.
— In case of 413, only one branch will be extended as the number is prime factorized as 7×59. 59 is a prime number and cannot be factored further.
Common mistakes and how to avoid them in factors of 413
We all make mistakes when it comes to finding factors, especially when it comes to numbers like 413. Don’t worry, it is a part of learning. Here are a few common slip-ups we may make, along with tips to avoid them.
Mistake 1
Excluding negative factors
Every positive factor has a corresponding negative factor. Often times, the negative factors are not included.
Factors of 413 Examples
Problem 1
If 413 is divisible by 7, find the missing factor in the pair (7,_).
Since 413÷7=59, the missing factor is 59.
So, the pair of factors is (7,59)
Explanation
When one factor is known, dividing the number by that factor gives the other factor. In this case, dividing 413 by 7 gives 59, revealing the pair (7,59).
Problem 2
Is 413 a prime number?
A prime number has only two factors: 1 and itself.
We’ve found that 413 has additional factors (1, 7, 59, and 413).
Therefore, 413 is not a prime number.
Explanation
A number is prime only if it has no other divisors except 1 and itself. Since we found that 413 is divisible by 7 and 59, it’s not prime.
Problem 3
What is the product of the largest and smallest factors of 413?
The smallest factor of 413 is 1, and the largest factor is 413.
Multiply these two factors: 1×413=413
So, the product of the largest and smallest factors is 413.
Explanation
The smallest and largest factors of any number are always 1 and the number itself. Multiplying them gives the original number, which is true for any non-zero integer.
FAQs on Factors of 413
1.What is the prime factorization of 143?
2. Is 69 a prime factor of 413?
3. What is the GCF of 413?
4. What is the prime factorization of 431?
5.What are the common factors of 413 and 295?
Important Glossaries for Factors of 413
- Factors: numbers that divide the given number without leaving a remainder.
- Prime factorization: breaking numbers down into their prime factors.
- Prime factors: Prime numbers that multiply together to form a given number.
- Composite number: Number that has at least more than one divisor other than 1 and the number itself.
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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.
