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Factors of 1950

Factors of 1950 are the list of integers that can be evenly divided into 1950. There are overall 24 factors of 1950, of which 2, 3, 5, 13 are its prime factors. The sum of all factors of 1950 is 5208.

All Factors of 1950: 1, 2, 3, 5, 6, 10, 13, 15, 25, 26, 30, 39, 50, 65, 75, 78, 130, 150, 195, 325, 390, 650, 975 and 1950
Prime Factors of 1950: 2, 3, 5, 13
Prime Factorization of 1950: 2¹ × 3¹ × 5² × 13¹
Sum of Factors of 1950: 5208

1.	What Are the Factors of 1950?
2.	Factors of 1950 by Prime Factorization
3.	Factors of 1950 in Pairs
4.	FAQs on Factors of 1950

What are Factors of 1950?

Factors of 1950 are pairs of those numbers whose products result in 1950. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1950?

To find the factors of 1950, we will have to find the list of numbers that would divide 1950 without leaving any remainder.

1950/5 = 390; therefore, 5 is a factor of 1950 and 390 is also a factor of 1950.
1950/325 = 6; therefore, 325 is a factor of 1950 and 6 is also a factor of 1950.

Similarly we can find other factors. Hence, the factors of 1950 are 1, 2, 3, 5, 6, 10, 13, 15, 25, 26, 30, 39, 50, 65, 75, 78, 130, 150, 195, 325, 390, 650, 975, 1950.

☛ Also Check:

Factors of 9 - The factors of 9 are 1, 3, 9
Factors of 16 - The factors of 16 are 1, 2, 4, 8, 16
Factors of 99 - The factors of 99 are 1, 3, 9, 11, 33, 99
Factors of 40 - The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40
Factors of 48 - The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Factors of 1950 by Prime Factorization

The number 1950 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1950. The first step is to divide the number 1950 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.

1950 ÷ 2 = 975

Further dividing 975 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 975 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 1950 can be written as 2¹ × 3¹ × 5² × 13¹ where 2, 3, 5, 13 are prime.

Factors of 1950 in Pairs

Pair factors of 1950 are the pairs of numbers that when multiplied give the product 1950. The factors of 1950 in pairs are:

1 × 1950 = (1, 1950)
2 × 975 = (2, 975)
3 × 650 = (3, 650)
5 × 390 = (5, 390)
6 × 325 = (6, 325)
10 × 195 = (10, 195)
13 × 150 = (13, 150)
15 × 130 = (15, 130)
25 × 78 = (25, 78)
26 × 75 = (26, 75)
30 × 65 = (30, 65)
39 × 50 = (39, 50)

Negative pair factors of 1950 are:

-1 × -1950 = (-1, -1950)
-2 × -975 = (-2, -975)
-3 × -650 = (-3, -650)
-5 × -390 = (-5, -390)
-6 × -325 = (-6, -325)
-10 × -195 = (-10, -195)
-13 × -150 = (-13, -150)
-15 × -130 = (-15, -130)
-25 × -78 = (-25, -78)
-26 × -75 = (-26, -75)
-30 × -65 = (-30, -65)
-39 × -50 = (-39, -50)

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

Factors of 1950 Solved Examples

Example 1: How many factors are there for 1950?

Solution:

The factors of 1950 are too many, therefore if we can find the prime factorization of 1950, 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 1950 = 2¹ × 3¹ × 5² × 13¹
Therefore, the total number of factors are (1 + 1) × (1 + 1) × (2 + 1) × (1 + 1) = 2 × 2 × 3 × 2 = 24
Example 2: Find the Least Common Multiple and Greatest Common Divisor (GCD) of 1950 and 62.

Solution:

The factors of 1950 are 1, 2, 3, 5, 6, 10, 13, 15, 25, 26, 30, 39, 50, 65, 75, 78, 130, 150, 195, 325, 390, 650, 975, 1950 and factors of 62 are 1, 2, 31, 62.

Therefore, the Least Common Multiple of 1950 and 62 is 60450 and Greatest Common Divisor (GCD) of 1950 and 62 is 2.
Example 3: Find if 3, 13, 30, 65, 130, 195, 975 and 1807 are factors of 1950.

Solution:

When we divide 1950 by 1807 it leaves a remainder. Therefore, the number 1807 is not a factor of 1950. All numbers except 1807 are factors of 1950.
Example 4: Find the product of all the prime factors of 1950.

Solution:

Since, the prime factors of 1950 are 2, 3, 5, 13. Therefore, the product of prime factors = 2 × 3 × 5 × 13 = 390.

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FAQs on Factors of 1950

What are the Factors of 1950?

The factors of 1950 are 1, 2, 3, 5, 6, 10, 13, 15, 25, 26, 30, 39, 50, 65, 75, 78, 130, 150, 195, 325, 390, 650, 975, 1950 and its negative factors are -1, -2, -3, -5, -6, -10, -13, -15, -25, -26, -30, -39, -50, -65, -75, -78, -130, -150, -195, -325, -390, -650, -975, -1950.

What is the Sum of all the Factors of 1950?

Sum of all factors of 1950 = (2^{1 + 1} - 1)/(2 - 1) × (3^{1 + 1} - 1)/(3 - 1) × (5^{2 + 1} - 1)/(5 - 1) × (13^{1 + 1} - 1)/(13 - 1) = 5208

What are the Pair Factors of 1950?

The pair factors of 1950 are (1, 1950), (2, 975), (3, 650), (5, 390), (6, 325), (10, 195), (13, 150), (15, 130), (25, 78), (26, 75), (30, 65), (39, 50).

What is the Greatest Common Factor of 1950 and 1852?

The factors of 1950 and 1852 are 1, 2, 3, 5, 6, 10, 13, 15, 25, 26, 30, 39, 50, 65, 75, 78, 130, 150, 195, 325, 390, 650, 975, 1950 and 1, 2, 4, 463, 926, 1852 respectively.

Common factors of 1950 and 1852 are [1, 2].

Hence, the Greatest Common Factor (GCF) of 1950 and 1852 is 2.

What are the Common Factors of 1950 and 110?

Since, the factors of 1950 are 1, 2, 3, 5, 6, 10, 13, 15, 25, 26, 30, 39, 50, 65, 75, 78, 130, 150, 195, 325, 390, 650, 975, 1950 and the factors of 110 are 1, 2, 5, 10, 11, 22, 55, 110.
Hence, [1, 2, 5, 10] are the common factors of 1950 and 110.

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