Factors of 1150

Factors of 1150 are the list of integers that can be evenly divided into 1150. There are total 12 factors of 1150, of which 2, 5, 23 are its prime factors. The sum of all factors of 1150 is 2232.

All Factors of 1150: 1, 2, 5, 10, 23, 25, 46, 50, 115, 230, 575 and 1150
Prime Factors of 1150: 2, 5, 23
Prime Factorization of 1150: 2¹ × 5² × 23¹
Sum of Factors of 1150: 2232

1.	What Are the Factors of 1150?
2.	Factors of 1150 by Prime Factorization
3.	Factors of 1150 in Pairs
4.	FAQs on Factors of 1150

What are Factors of 1150?

Factors of 1150 are pairs of those numbers whose products result in 1150. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1150?

To find the factors of 1150, we will have to find the list of numbers that would divide 1150 without leaving any remainder.

1150/115 = 10; therefore, 115 is a factor of 1150 and 10 is also a factor of 1150.
1150/2 = 575; therefore, 2 is a factor of 1150 and 575 is also a factor of 1150.

Similarly we can find other factors. Hence, the factors of 1150 are 1, 2, 5, 10, 23, 25, 46, 50, 115, 230, 575, 1150.

☛ Also Check:

Factors of 20 - The factors of 20 are 1, 2, 4, 5, 10, 20
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 57 - The factors of 57 are 1, 3, 19, 57
Factors of 32 - The factors of 32 are 1, 2, 4, 8, 16, 32
Factors of 75 - The factors of 75 are 1, 3, 5, 15, 25, 75

Factors of 1150 by Prime Factorization

The number 1150 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1150. The first step is to divide the number 1150 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.

1150 ÷ 2 = 575

Further dividing 575 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 575 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 1150 can be written as 2¹ × 5² × 23¹ where 2, 5, 23 are prime.

Factors of 1150 in Pairs

Pair factors of 1150 are the pairs of numbers that when multiplied give the product 1150. The factors of 1150 in pairs are:

1 × 1150 = (1, 1150)
2 × 575 = (2, 575)
5 × 230 = (5, 230)
10 × 115 = (10, 115)
23 × 50 = (23, 50)
25 × 46 = (25, 46)

Negative pair factors of 1150 are:

-1 × -1150 = (-1, -1150)
-2 × -575 = (-2, -575)
-5 × -230 = (-5, -230)
-10 × -115 = (-10, -115)
-23 × -50 = (-23, -50)
-25 × -46 = (-25, -46)

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

Factors of 1150 Solved Examples

Example 1: How many factors are there for 1150?

Solution:

The factors of 1150 are too many, therefore if we can find the prime factorization of 1150, 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 1150 = 2¹ × 5² × 23¹
Therefore, the total number of factors are (1 + 1) × (2 + 1) × (1 + 1) = 2 × 3 × 2 = 12
Example 2: Find the Lowest Common Multiple (LCM) and Greatest Common Factor (GCF) of 1150 and 719.

Solution:

The factors of 1150 are 1, 2, 5, 10, 23, 25, 46, 50, 115, 230, 575, 1150 and factors of 719 are 1, 719.

Therefore, the Lowest Common Multiple (LCM) of 1150 and 719 is 826850 and Greatest Common Factor (GCF) of 1150 and 719 is 1.
Example 3: Find if 1, 3, 10, 46, 230, 575 and 1150 are factors of 1150.

Solution:

When we divide 1150 by 3 it leaves a remainder. Therefore, the number 3 is not a factor of 1150. All numbers except 3 are factors of 1150.
Example 4: Find the product of all the prime factors of 1150.

Solution:

Since, the prime factors of 1150 are 2, 5, 23. Therefore, the product of prime factors = 2 × 5 × 23 = 230.

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FAQs on Factors of 1150

What are the Factors of 1150?

The factors of 1150 are 1, 2, 5, 10, 23, 25, 46, 50, 115, 230, 575, 1150 and its negative factors are -1, -2, -5, -10, -23, -25, -46, -50, -115, -230, -575, -1150.

What is the Sum of all the Factors of 1150?

Sum of all factors of 1150 = (2^{1 + 1} - 1)/(2 - 1) × (5^{2 + 1} - 1)/(5 - 1) × (23^{1 + 1} - 1)/(23 - 1) = 2232

What Numbers are the Prime Factors of 1150?

The prime factors of 1150 are 2, 5, 23.

What is the Greatest Common Factor of 1150 and 267?

The factors of 1150 are 1, 2, 5, 10, 23, 25, 46, 50, 115, 230, 575, 1150 and the factors of 267 are 1, 3, 89, 267. 1150 and 267 have only one common factor which is 1. This implies that 1150 and 267 are co-prime.

Hence, the Greatest Common Factor (GCF) of 1150 and 267 is 1.

How Many Factors of 1150 are also common to the Factors of 270?

Since, the factors of 1150 are 1, 2, 5, 10, 23, 25, 46, 50, 115, 230, 575, 1150 and the factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270.
Hence, [1, 2, 5, 10] are the common factors of 1150 and 270.

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