217 LearnersLast updated on May 26th, 2025
Factors of 496
Factors are the ‘building blocks’ of a number. They are the numbers that can be multiplied together to reach the number you started with. 496 is not 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 496?
Factors are whole numbers that, when multiplied, the product is equal to 496.
496 is not a prime number, its only factors are 1,2,4,8,16,31,62,124,248,496. For every factor, there is not a corresponding negative factor, for 496, the negative factors are -1,-2,-4,-8,-16,-31,-62,-124,-248,-496.
How to find the factors of 496?
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 496.
Step 2: All the pairs found represent the factors of 496.
496 is not a prime number. The pair of numbers whose product is 496 is
1×496=496
2×248 =496
4×124=496
8×62=496
16×31=496
The factors of 496 are 1,2,4,8,16,31,62,124,248,496.
Finding Factors by Division Method
Step 1: Start by dividing 496 with the smallest number, and check the remainders.
Step 2: 496 is prime, therefore the only divisors it has are 1,2,4,8,16,31,62,124,248,496. Any number that is further checked for divisibility leaves behind a remainder.
The factors of 496 are 1,2,4,8,16,31,62,124,248,496.
Prime factors and prime factorization
— 496 is not a prime number.
— The prime factorization of 496 is 24 ×311. 2 and 31 are prime factors of 496.
— Factors of 496 are 1,2,4,8,16,31,62,124,248,496
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 496, first branch will be — 2×248 → 2×124 → 2×62 → 2×31 — the factorization ends here, 31 is a prime number.
Common mistakes and how to avoid them in factors of 496
We all make mistakes when it comes to finding factors, especially when it comes to numbers like 496. Don’t worry, it is not 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 496 Examples
Problem 1
What is the sum of all the factors of 496?
List all factors of 496: 1, 2, 4, 8, 16, 31, 62, 124, 248, and 496.
Add them together: 1+2+4+8+16+31+62+124+248+496=992
So, the sum of all factors of 496 is 992.
Explanation
To find the sum of all factors, list each factor and add them up. Summing factors can help in number theory problems, where we might need to know if the sum of factors equals a certain number.
Problem 2
Is 496 a perfect number? (A perfect number equals the sum of all its factors excluding itself.)
List the factors of 496 excluding 496 itself: 1, 2, 4, 8, 16, 31, 62, 124, and 248.
Find the sum: 1+2+4+8+16+31+62+124+248=496
Since the sum of the factors (excluding 496) equals 496, 496 is a perfect number.
Explanation
A perfect number equals the sum of its factors, excluding itself. We calculated the sum and found it equals 496, so 496 is perfect—a unique property!
Problem 3
Find the greatest common factor (GCF) of 496 and 124.
List the factors of each number:
Factors of 496: 1, 2, 4, 8, 16, 31, 62, 124, 248, 496.
Factors of 124: 1, 2, 4, 8, 31, 62, 124.
The common factors are 1, 2, 4, 8, 31, 62, and 124.
The greatest common factor is 124.
Explanation
To find the GCF, we list the factors of both numbers and look for the largest one they share. Here, 124 is the largest number that divides both 496 and 124.
Problem 4
What is the product of all unique prime factors of 496?
From the prime factorization, we know that 496 = 24×31
The unique prime factors are 2 and 31.
Product of unique prime factors: 2×31=62
Explanation
For unique prime factors, we only consider each prime once (ignoring the exponents). Multiplying these unique primes gives a product of 62.
FAQs on Factors of 496
1.What are the factors of 469?
2.What are the multiples of 496?
3.Why is 496 a perfect number?
4.What is the GCF of 496 and 2080?
5.Is the cube root of 496 rational?
Important Glossaries for Factors of 496
- 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.
