A day full of math games & activities. Find one near you.

Factors of 460

Factors of 460 are the list of integers that we can split evenly into 460. There are overall 12 factors of 460 among which 460 is the biggest factor and 2, 5, 23 are its prime factors. The Prime Factorization of 460 is 2² × 5¹ × 23¹.

All Factors of 460: 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230 and 460
Prime Factors of 460: 2, 5, 23
Prime Factorization of 460: 2² × 5¹ × 23¹
Sum of Factors of 460: 1008

1.	What Are the Factors of 460?
2.	Factors of 460 by Prime Factorization
3.	Factors of 460 in Pairs
4.	FAQs on Factors of 460

What are Factors of 460?

Factors of 460 are pairs of those numbers whose products result in 460. These factors are either prime numbers or composite numbers.

How to Find the Factors of 460?

To find the factors of 460, we will have to find the list of numbers that would divide 460 without leaving any remainder.

460/10 = 46; therefore, 10 is a factor of 460 and 46 is also a factor of 460.
460/23 = 20; therefore, 23 is a factor of 460 and 20 is also a factor of 460.

Similarly we can find other factors. Hence, the factors of 460 are 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460.

☛ Also Check:

Factors of 125 - The factors of 125 are 1, 5, 25, 125
Factors of 19 - The factors of 19 are 1, 19
Factors of 35 - The factors of 35 are 1, 5, 7, 35
Factors of 16 - The factors of 16 are 1, 2, 4, 8, 16
Factors of 121 - The factors of 121 are 1, 11, 121

Factors of 460 by Prime Factorization

The number 460 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 460. The first step is to divide the number 460 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.

460 ÷ 2 = 230
230 ÷ 2 = 115

Further dividing 115 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 115 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 460 can be written as 2² × 5¹ × 23¹ where 2, 5, 23 are prime.

Factors of 460 in Pairs

Pair factors of 460 are the pairs of numbers that when multiplied give the product 460. The factors of 460 in pairs are:

1 × 460 = (1, 460)
2 × 230 = (2, 230)
4 × 115 = (4, 115)
5 × 92 = (5, 92)
10 × 46 = (10, 46)
20 × 23 = (20, 23)

Negative pair factors of 460 are:

-1 × -460 = (-1, -460)
-2 × -230 = (-2, -230)
-4 × -115 = (-4, -115)
-5 × -92 = (-5, -92)
-10 × -46 = (-10, -46)
-20 × -23 = (-20, -23)

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

Factors of 460 Solved Examples

Example 1: How many factors are there for 460?

Solution:

The factors of 460 are too many, therefore if we can find the prime factorization of 460, 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 460 = 2² × 5¹ × 23¹
Therefore, the total number of factors are (2 + 1) × (1 + 1) × (1 + 1) = 3 × 2 × 2 = 12
Example 2: Find the Least Common Multiple and Greatest Common Divisor (GCD) of 460 and 449.

Solution:

The factors of 460 are 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460 and factors of 449 are 1, 449.

Therefore, the Least Common Multiple of 460 and 449 is 206540 and Greatest Common Divisor (GCD) of 460 and 449 is 1.
Example 3: Find if 1, 4, 20, 23, 115, 149 and 460 are factors of 460.

Solution:

When we divide 460 by 149 it leaves a remainder. Therefore, the number 149 is not a factor of 460. All numbers except 149 are factors of 460.
Example 4: Find the product of all the prime factors of 460.

Solution:

Since, the prime factors of 460 are 2, 5, 23. Therefore, the product of prime factors = 2 × 5 × 23 = 230.

go to slide go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

go to slide go to slide go to slide go to slide go to slide

FAQs on Factors of 460

What are the Factors of 460?

The factors of 460 are 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460 and its negative factors are -1, -2, -4, -5, -10, -20, -23, -46, -92, -115, -230, -460.

What is the Sum of all the Factors of 460?

Sum of all factors of 460 = (2^{2 + 1} - 1)/(2 - 1) × (5^{1 + 1} - 1)/(5 - 1) × (23^{1 + 1} - 1)/(23 - 1) = 1008

What Numbers are the Prime Factors of 460?

The prime factors of 460 are 2, 5, 23.

What is the Greatest Common Factor of 460 and 423?

The factors of 460 are 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460 and the factors of 423 are 1, 3, 9, 47, 141, 423. 460 and 423 have only one common factor which is 1. This implies that 460 and 423 are co-prime.

Hence, the Greatest Common Factor (GCF) of 460 and 423 is 1.

How Many Factors of 460 are also common to the Factors of 323?

Since, the factors of 460 are 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460 and factors of 323 are 1, 17, 19, 323. Hence, 460 and 323 have only one common factor which is 1. Therefore, 460 and 323 are co-prime.

Math worksheets and
visual curriculum