1. Steps to find factors of 1950 using Division Method

Example: Find factors of 1950

  • Divide 1950 by 1: 1950 ÷ 1 : Remainder = 0
  • Divide 1950 by 2: 1950 ÷ 2 : Remainder = 0
  • Divide 1950 by 3: 1950 ÷ 3 : Remainder = 0
  • Divide 1950 by 5: 1950 ÷ 5 : Remainder = 0
  • Divide 1950 by 6: 1950 ÷ 6 : Remainder = 0
  • Divide 1950 by 10: 1950 ÷ 10 : Remainder = 0
  • Divide 1950 by 13: 1950 ÷ 13 : Remainder = 0
  • Divide 1950 by 15: 1950 ÷ 15 : Remainder = 0
  • Divide 1950 by 25: 1950 ÷ 25 : Remainder = 0
  • Divide 1950 by 26: 1950 ÷ 26 : Remainder = 0
  • Divide 1950 by 30: 1950 ÷ 30 : Remainder = 0
  • Divide 1950 by 39: 1950 ÷ 39 : Remainder = 0
  • Divide 1950 by 50: 1950 ÷ 50 : Remainder = 0
  • Divide 1950 by 65: 1950 ÷ 65 : Remainder = 0
  • Divide 1950 by 75: 1950 ÷ 75 : Remainder = 0
  • Divide 1950 by 78: 1950 ÷ 78 : Remainder = 0
  • Divide 1950 by 130: 1950 ÷ 130 : Remainder = 0
  • Divide 1950 by 150: 1950 ÷ 150 : Remainder = 0
  • Divide 1950 by 195: 1950 ÷ 195 : Remainder = 0
  • Divide 1950 by 325: 1950 ÷ 325 : Remainder = 0
  • Divide 1950 by 390: 1950 ÷ 390 : Remainder = 0
  • Divide 1950 by 650: 1950 ÷ 650 : Remainder = 0
  • Divide 1950 by 975: 1950 ÷ 975 : Remainder = 0
  • Divide 1950 by 1950: 1950 ÷ 1950 : Remainder = 0

Hence, 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, and 1950

2. Steps to find factors of 1950 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

Method 1: Division Method

To find the primefactors of 1950 using the division method, follow these steps:

  • Step 1. Start dividing 1950 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
  • Step 2. After finding the smallest prime factor of the number 1950, which is 2. Divide 1950 by 2 to obtain the quotient (975).
    1950 ÷ 2 = 975
  • Step 3. Repeat step 1 with the obtained quotient (975).
    975 ÷ 3 = 325
    325 ÷ 5 = 65
    65 ÷ 5 = 13
    13 ÷ 13 = 1

So, the prime factorization of 1950 is, 1950 = 2 x 3 x 5 x 5 x 13.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1950 as shown below:

So, the prime factorization of 1950 is, 1950 = 2 x 3 x 5 x 5 x 13.

3. Find factors of 1950 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 1950 would be the two numbers which, when multiplied, give 1950 as the result.

The following table represents the calculation of factors of 1950 in pairs:

Factor Pair Pair Factorization
1 and 1950 1 x 1950 = 1950
2 and 975 2 x 975 = 1950
3 and 650 3 x 650 = 1950
5 and 390 5 x 390 = 1950
6 and 325 6 x 325 = 1950
10 and 195 10 x 195 = 1950
13 and 150 13 x 150 = 1950
15 and 130 15 x 130 = 1950
25 and 78 25 x 78 = 1950
26 and 75 26 x 75 = 1950
30 and 65 30 x 65 = 1950
39 and 50 39 x 50 = 1950

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 1950. They are called negative pair factors.

Hence, the negative pairs of 1950 would be ( -1 , -1950 ) , ( -2 , -975 ) , ( -3 , -650 ) , ( -5 , -390 ) , ( -6 , -325 ) , ( -10 , -195 ) , ( -13 , -150 ) , ( -15 , -130 ) , ( -25 , -78 ) , ( -26 , -75 ) , ( -30 , -65 ) and ( -39 , -50 ) .

What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

Properties of factors

  • Each number is a factor of itself. Eg. 1950 is a factor of itself.
  • Every number other than 1 has at least two factors, namely the number itself and 1.
  • Every factor of a number is an exact divisor of that number, example 1, 2, 3, 5, 6, 10, 13, 15, 25, 26, 30, 39, 50, 65, 75, 78, 130, 150, 195, 325, 390, 650, 975, 1950 are exact divisors of 1950.
  • 1 is a factor of every number. Eg. 1 is a factor of 1950.
  • Every number is a factor of zero (0), since 1950 x 0 = 0.

Frequently Asked Questions

  • How do you find factors of a negative number? ( eg. -1950 )?

    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.

  • What is the sum of all factors of 1950?

    The sum of all factors of 1950 is 5208.

  • What is prime factorization of 1950?

    Prime factorization of 1950 is 2 x 3 x 5 x 5 x 13.

  • What are the pair factors of 1950?

    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 are six multiples of 1950?

    First five multiples of 1950 are 3900, 5850, 7800, 9750, 11700, 13650.

  • Is 1950 a whole number?

    Yes 1950 is a whole number.

  • Which is the smallest prime factor of 1950?

    Smallest prime factor of 1950 is 2.

  • What are five multiples of 1950?

    First five multiples of 1950 are 3900, 5850, 7800, 9750, 11700.

  • Write all factors of 1950?

    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.

Examples of Factors

Joey wants to write all the prime factors of 1950 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1950 are 2, 3, 5, 5, 13.
So in exponential form it can be written as 2 x 3 x 52 x 13.

How many factors are there for 1950?

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.
So there are in total 24 factors.

Kevin has been asked to write 23 factor(s) of 1950. Can you predict the answer?

23 factor(s) 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.

Sammy is puzzled while calculating the prime factors of 1950. Can you help him find them?

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.
Prime factors of 1950 are 2, 3, 5, 5, 13

What is prime factorization of 1950?

Prime factorization of 1950 is 2 x 3 x 5 x 5 x 13 = 2 x 3 x 52 x 13.

Ariel has been assigned the task to find the product of all the prime factors of 1950. Can you help her?

Prime factors of 1950 are 2, 3, 5, 5, 13.
Hence, the product of prime factors of 390.

Can you help Rubel to find out the product of the even factors of 1950?

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.
Even factors of 1950 are 2, 6, 10, 26, 30, 50, 78, 130, 150, 390, 650, 1950.
Hence, product of even factors of 1950 is; 2 x 6 x 10 x 26 x 30 x 50 x 78 x 130 x 150 x 390 x 650 x 1950 = 3.518743761e+21.