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Factors of 496

Factors of 496 are numbers that, when multiplied in pairs give the product as 496. There are 10 factors of 496 of which 496 itself is the biggest factor and its prime factors are 2, 31 The sum of all factors of 496 is 992.

All Factors of 496: 1, 2, 4, 8, 16, 31, 62, 124, 248 and 496
Negative Factors of 496: -1, -2, -4, -8, -16, -31, -62, -124, -248 and -496
Prime Factors of 496: 2, 31
Prime Factorization of 496: 2⁴ × 31¹
Sum of Factors of 496: 992

1.	What Are the Factors of 496?
2.	Factors of 496 by Prime Factorization
3.	Factors of 496 in Pairs
4.	FAQs on Factors of 496

What are Factors of 496?

Factors of 496 are pairs of those numbers whose products result in 496. These factors are either prime numbers or composite numbers.

How to Find the Factors of 496?

To find the factors of 496, we will have to find the list of numbers that would divide 496 without leaving any remainder.

496/248 = 2; therefore, 248 is a factor of 496 and 2 is also a factor of 496.
496/124 = 4; therefore, 124 is a factor of 496 and 4 is also a factor of 496.

Similarly we can find other factors. Hence, the factors of 496 are 1, 2, 4, 8, 16, 31, 62, 124, 248, 496.

☛ Also Check:

Factors of 24 - The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
Factors of 15 - The factors of 15 are 1, 3, 5, 15
Factors of 11 - The factors of 11 are 1, 11
Factors of 12 - The factors of 12 are 1, 2, 3, 4, 6, 12
Factors of 144 - The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144

Factors of 496 by Prime Factorization

The number 496 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 496. The first step is to divide the number 496 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.

496 ÷ 2 = 248
248 ÷ 2 = 124
124 ÷ 2 = 62
62 ÷ 2 = 31

Further dividing 31 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 31 by the next smallest prime factor. We stop ultimately if the next prime factor doesn't exist or when we can't divide any further.

So, the prime factorization of 496 can be written as 2⁴ × 31¹ where 2, 31 are prime.

Factors of 496 in Pairs

Pair factors of 496 are the pairs of numbers that when multiplied give the product 496. The factors of 496 in pairs are:

1 × 496 = (1, 496)
2 × 248 = (2, 248)
4 × 124 = (4, 124)
8 × 62 = (8, 62)
16 × 31 = (16, 31)

Negative pair factors of 496 are:

-1 × -496 = (-1, -496)
-2 × -248 = (-2, -248)
-4 × -124 = (-4, -124)
-8 × -62 = (-8, -62)
-16 × -31 = (-16, -31)

NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.

Factors of 496 Solved Examples

Example 1: How many factors are there for 496?

Solution:

The factors of 496 are too many, therefore if we can find the prime factorization of 496, then the total number of factors can be calculated using the formula shown below.
If the prime factorization of the number is a^x × b^y × c^z where a, b, c are prime, then the total number of factors can be given by (x + 1)(y + 1)(z + 1).

Prime Factorization of 496 = 2⁴ × 31¹
Therefore, the total number of factors are (4 + 1) × (1 + 1) = 5 × 2 = 10
Example 2: Find the LCM and Greatest Common Divisor (GCD) of 496 and 218.

Solution:

The factors of 496 are 1, 2, 4, 8, 16, 31, 62, 124, 248, 496 and factors of 218 are 1, 2, 109, 218.

Therefore, the LCM of 496 and 218 is 54064 and Greatest Common Divisor (GCD) of 496 and 218 is 2.
Example 3: Find if 2, 8, 31, 124, 341 and 496 are factors of 496.

Solution:

When we divide 496 by 341 it leaves a remainder. Therefore, the number 341 is not a factor of 496. All numbers except 341 are factors of 496.
Example 4: Find the product of all the prime factors of 496.

Solution:

Since, the prime factors of 496 are 2, 31. Therefore, the product of prime factors = 2 × 31 = 62.

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FAQs on Factors of 496

What are the Factors of 496?

The factors of 496 are 1, 2, 4, 8, 16, 31, 62, 124, 248, 496 and its negative factors are -1, -2, -4, -8, -16, -31, -62, -124, -248, -496.

What is the Sum of the Factors of 496?

Sum of all factors of 496 = (2^{4 + 1} - 1)/(2 - 1) × (31^{1 + 1} - 1)/(31 - 1) = 992

What are Pair Factors of 496?

The pair factors of 496 are (1, 496), (2, 248), (4, 124), (8, 62), (16, 31).

What is the Greatest Common Factor of 496 and 317?

The factors of 496 are 1, 2, 4, 8, 16, 31, 62, 124, 248, 496 and the factors of 317 are 1, 317. 496 and 317 have only one common factor which is 1. This implies that 496 and 317 are co-prime.

Hence, the Greatest Common Factor (GCF) of 496 and 317 is 1.

What are the Common Factors of 496 and 376?

Since, the factors of 496 are 1, 2, 4, 8, 16, 31, 62, 124, 248, 496 and the factors of 376 are 1, 2, 4, 8, 47, 94, 188, 376.
Hence, [1, 2, 4, 8] are the common factors of 496 and 376.

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