Factors of 750
Factors of 750 are the list of integers that can be evenly divided into 750. There are 16 factors of 750, of which the following are its prime factors 2, 3, 5. The Prime Factorization of 750 is 21 × 31 × 53.
- All Factors of 750: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375 and 750
- Prime Factors of 750: 2, 3, 5
- Prime Factorization of 750: 21 × 31 × 53
- Sum of Factors of 750: 1872
1. | What Are the Factors of 750? |
2. | Factors of 750 by Prime Factorization |
3. | Factors of 750 in Pairs |
4. | FAQs on Factors of 750 |
What are Factors of 750?
Factors of 750 are pairs of those numbers whose products result in 750. These factors are either prime numbers or composite numbers.
How to Find the Factors of 750?
To find the factors of 750, we will have to find the list of numbers that would divide 750 without leaving any remainder.
- 750/3 = 250; therefore, 3 is a factor of 750 and 250 is also a factor of 750.
- 750/15 = 50; therefore, 15 is a factor of 750 and 50 is also a factor of 750.
☛ Also Check:
- Factors of 52 - The factors of 52 are 1, 2, 4, 13, 26, 52
- Factors of 10 - The factors of 10 are 1, 2, 5, 10
- Factors of 98 - The factors of 98 are 1, 2, 7, 14, 49, 98
- Factors of 90 - The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
- Factors of 26 - The factors of 26 are 1, 2, 13, 26
Factors of 750 by Prime Factorization
- 750 ÷ 2 = 375
Further dividing 375 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 375 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 750 can be written as 21 × 31 × 53 where 2, 3, 5 are prime.
Factors of 750 in Pairs
Pair factors of 750 are the pairs of numbers that when multiplied give the product 750. The factors of 750 in pairs are:
- 1 × 750 = (1, 750)
- 2 × 375 = (2, 375)
- 3 × 250 = (3, 250)
- 5 × 150 = (5, 150)
- 6 × 125 = (6, 125)
- 10 × 75 = (10, 75)
- 15 × 50 = (15, 50)
- 25 × 30 = (25, 30)
Negative pair factors of 750 are:
- -1 × -750 = (-1, -750)
- -2 × -375 = (-2, -375)
- -3 × -250 = (-3, -250)
- -5 × -150 = (-5, -150)
- -6 × -125 = (-6, -125)
- -10 × -75 = (-10, -75)
- -15 × -50 = (-15, -50)
- -25 × -30 = (-25, -30)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 750 Solved Examples
-
Example 1: How many factors are there for 750?
Solution:
The factors of 750 are too many, therefore if we can find the prime factorization of 750, then the total number of factors can be calculated using the formula shown below.
If the prime factorization of the number is ax × by × cz 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 750 = 21 × 31 × 53
Therefore, the total number of factors are (1 + 1) × (1 + 1) × (3 + 1) = 2 × 2 × 4 = 16 -
Example 2: Find the Least Common Multiple and Highest Common Factor (HCF) of 750 and 697.
Solution:
The factors of 750 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, 750 and factors of 697 are 1, 17, 41, 697.
Therefore, the Least Common Multiple of 750 and 697 is 522750 and Highest Common Factor (HCF) of 750 and 697 is 1. -
Example 3: Find if 10, 30, 50, 125, 150, 250, 415 and 750 are factors of 750.
Solution:
When we divide 750 by 415 it leaves a remainder. Therefore, the number 415 is not a factor of 750. All numbers except 415 are factors of 750.
-
Example 4: Find the product of all the prime factors of 750.
Solution:
Since, the prime factors of 750 are 2, 3, 5. Therefore, the product of prime factors = 2 × 3 × 5 = 30.
FAQs on Factors of 750
What are the Factors of 750?
The factors of 750 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, 750 and its negative factors are -1, -2, -3, -5, -6, -10, -15, -25, -30, -50, -75, -125, -150, -250, -375, -750.
What is the Sum of all the Factors of 750?
Sum of all factors of 750 = (21 + 1 - 1)/(2 - 1) × (31 + 1 - 1)/(3 - 1) × (53 + 1 - 1)/(5 - 1) = 1872
What Numbers are the Prime Factors of 750?
The prime factors of 750 are 2, 3, 5.
What is the Greatest Common Factor of 750 and 301?
The factors of 750 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, 750 and the factors of 301 are 1, 7, 43, 301. 750 and 301 have only one common factor which is 1. This implies that 750 and 301 are co-prime.
Hence, the Greatest Common Factor (GCF) of 750 and 301 is 1.
How Many Factors of 750 are also common to the Factors of 425?
Since, the factors of 750 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, 750 and the factors of 425 are 1, 5, 17, 25, 85, 425.
Hence, [1, 5, 25] are the common factors of 750 and 425.
visual curriculum