Factors of 350 are integers that can be divided evenly into 350. There are overall 12 factors of 350 among which 350 is the biggest factor and 2, 5, 7 are its prime factors. The sum of all factors of 350 is 744.
- All Factors of 350: 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175 and 350
- Prime Factors of 350: 2, 5, 7
- Prime Factorization of 350: 21 × 52 × 71
- Sum of Factors of 350: 744
| 1. | What Are the Factors of 350? |
| 2. | Factors of 350 by Prime Factorization |
| 3. | Factors of 350 in Pairs |
| 4. | FAQs on Factors of 350 |
What are Factors of 350?
Factors of 350 are pairs of those numbers whose products result in 350. These factors are either prime numbers or composite numbers.
How to Find the Factors of 350?
To find the factors of 350, we will have to find the list of numbers that would divide 350 without leaving any remainder.
- 350/175 = 2; therefore, 175 is a factor of 350 and 2 is also a factor of 350.
- 350/35 = 10; therefore, 35 is a factor of 350 and 10 is also a factor of 350.
Similarly we can find other factors. Hence, the factors of 350 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350.
☛ Also Check:
- Factors of 41 - The factors of 41 are 1, 41
- Factors of 91 - The factors of 91 are 1, 7, 13, 91
- Factors of 84 - The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
- Factors of 180 - The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
- Factors of 9 - The factors of 9 are 1, 3, 9
Factors of 350 by Prime Factorization
The number 350 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 350. The first step is to divide the number 350 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
- 350 ÷ 2 = 175
Further dividing 175 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 175 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 350 can be written as 21 × 52 × 71 where 2, 5, 7 are prime.
Factors of 350 in Pairs
Pair factors of 350 are the pairs of numbers that when multiplied give the product 350. The factors of 350 in pairs are:
- 1 × 350 = (1, 350)
- 2 × 175 = (2, 175)
- 5 × 70 = (5, 70)
- 7 × 50 = (7, 50)
- 10 × 35 = (10, 35)
- 14 × 25 = (14, 25)
Negative pair factors of 350 are:
- -1 × -350 = (-1, -350)
- -2 × -175 = (-2, -175)
- -5 × -70 = (-5, -70)
- -7 × -50 = (-7, -50)
- -10 × -35 = (-10, -35)
- -14 × -25 = (-14, -25)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 350 Solved Examples
Example 1: How many factors are there for 350?
Solution:
The factors of 350 are too many, therefore if we can find the prime factorization of 350, 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 350 = 21 × 52 × 71
Therefore, the total number of factors are (1 + 1) × (2 + 1) × (1 + 1) = 2 × 3 × 2 = 12Example 2: Find the LCM and Greatest Common Divisor (GCD) of 350 and 160.
Solution:
The factors of 350 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350 and factors of 160 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160.
Therefore, the LCM of 350 and 160 is 5600 and Greatest Common Divisor (GCD) of 350 and 160 is 10.
Example 3: Find if 5, 10, 25, 32, 50, 70 and 175 are factors of 350.
Solution:
When we divide 350 by 32 it leaves a remainder. Therefore, the number 32 is not a factor of 350. All numbers except 32 are factors of 350.
Example 4: Find the product of all the prime factors of 350.
Solution:
Since, the prime factors of 350 are 2, 5, 7. Therefore, the product of prime factors = 2 × 5 × 7 = 70.
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FAQs on Factors of 350
What are the Factors of 350?
The factors of 350 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350 and its negative factors are -1, -2, -5, -7, -10, -14, -25, -35, -50, -70, -175, -350.
What is the Sum of the Factors of 350?
Sum of all factors of 350 = (21 + 1 - 1)/(2 - 1) × (52 + 1 - 1)/(5 - 1) × (71 + 1 - 1)/(7 - 1) = 744
What are Pair Factors of 350?
The pair factors of 350 are (1, 350), (2, 175), (5, 70), (7, 50), (10, 35), (14, 25).
What is the Greatest Common Factor of 350 and 77?
The factors of 350 and 77 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350 and 1, 7, 11, 77 respectively.
Common factors of 350 and 77 are [1, 7].
Hence, the Greatest Common Factor of 350 and 77 is 7.
How Many Factors of 350 are also Factors of 51?
Since, the factors of 350 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350 and factors of 51 are 1, 3, 17, 51. Hence, 350 and 51 have only one common factor which is 1. Therefore, 350 and 51 are co-prime.
