1. Steps to find factors of 2450 using Division Method

Example: Find factors of 2450

  • Divide 2450 by 1: 2450 ÷ 1 : Remainder = 0
  • Divide 2450 by 2: 2450 ÷ 2 : Remainder = 0
  • Divide 2450 by 5: 2450 ÷ 5 : Remainder = 0
  • Divide 2450 by 7: 2450 ÷ 7 : Remainder = 0
  • Divide 2450 by 10: 2450 ÷ 10 : Remainder = 0
  • Divide 2450 by 14: 2450 ÷ 14 : Remainder = 0
  • Divide 2450 by 25: 2450 ÷ 25 : Remainder = 0
  • Divide 2450 by 35: 2450 ÷ 35 : Remainder = 0
  • Divide 2450 by 49: 2450 ÷ 49 : Remainder = 0
  • Divide 2450 by 50: 2450 ÷ 50 : Remainder = 0
  • Divide 2450 by 70: 2450 ÷ 70 : Remainder = 0
  • Divide 2450 by 98: 2450 ÷ 98 : Remainder = 0
  • Divide 2450 by 175: 2450 ÷ 175 : Remainder = 0
  • Divide 2450 by 245: 2450 ÷ 245 : Remainder = 0
  • Divide 2450 by 350: 2450 ÷ 350 : Remainder = 0
  • Divide 2450 by 490: 2450 ÷ 490 : Remainder = 0
  • Divide 2450 by 1225: 2450 ÷ 1225 : Remainder = 0
  • Divide 2450 by 2450: 2450 ÷ 2450 : Remainder = 0

Hence, Factors of 2450 are 1, 2, 5, 7, 10, 14, 25, 35, 49, 50, 70, 98, 175, 245, 350, 490, 1225, and 2450

2. Steps to find factors of 2450 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 2450 using the division method, follow these steps:

  • Step 1. Start dividing 2450 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 2450, which is 2. Divide 2450 by 2 to obtain the quotient (1225).
    2450 ÷ 2 = 1225
  • Step 3. Repeat step 1 with the obtained quotient (1225).
    1225 ÷ 5 = 245
    245 ÷ 5 = 49
    49 ÷ 7 = 7
    7 ÷ 7 = 1

So, the prime factorization of 2450 is, 2450 = 2 x 5 x 5 x 7 x 7.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 2450 as shown below:

So, the prime factorization of 2450 is, 2450 = 2 x 5 x 5 x 7 x 7.

3. Find factors of 2450 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 2450 would be the two numbers which, when multiplied, give 2450 as the result.

The following table represents the calculation of factors of 2450 in pairs:

Factor Pair Pair Factorization
1 and 2450 1 x 2450 = 2450
2 and 1225 2 x 1225 = 2450
5 and 490 5 x 490 = 2450
7 and 350 7 x 350 = 2450
10 and 245 10 x 245 = 2450
14 and 175 14 x 175 = 2450
25 and 98 25 x 98 = 2450
35 and 70 35 x 70 = 2450
49 and 50 49 x 50 = 2450

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 2450. They are called negative pair factors.

Hence, the negative pairs of 2450 would be ( -1 , -2450 ) , ( -2 , -1225 ) , ( -5 , -490 ) , ( -7 , -350 ) , ( -10 , -245 ) , ( -14 , -175 ) , ( -25 , -98 ) , ( -35 , -70 ) and ( -49 , -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. 2450 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, 5, 7, 10, 14, 25, 35, 49, 50, 70, 98, 175, 245, 350, 490, 1225, 2450 are exact divisors of 2450.
  • 1 is a factor of every number. Eg. 1 is a factor of 2450.
  • Every number is a factor of zero (0), since 2450 x 0 = 0.

Frequently Asked Questions

  • What two numbers make 2450?

    Two numbers that make 2450 are 2 and 1225.

  • What is prime factorization of 2450?

    Prime factorization of 2450 is 2 x 5 x 5 x 7 x 7.

  • Write some multiples of 2450?

    First five multiples of 2450 are 4900, 7350, 9800, 12250.

  • Which is the smallest prime factor of 2450?

    The smallest prime factor of 2450 is 2.

  • Is 2450 a perfect square?

    No 2450 is not a perfect square.

  • What is the sum of all factors of 2450?

    The sum of all factors of 2450 is 5301.

  • What are factors of 2450?

    Factors of 2450 are 1, 2, 5, 7, 10, 14, 25, 35, 49, 50, 70, 98, 175, 245, 350, 490, 1225, 2450.

  • How do you find factors of a negative number? ( eg. -2450 )?

    Factors of -2450 are -1, -2, -5, -7, -10, -14, -25, -35, -49, -50, -70, -98, -175, -245, -350, -490, -1225, -2450.

  • Is 2450 a whole number?

    Yes 2450 is a whole number.

Examples of Factors

Joy wants to calculate mean of all the factors of 2450. Help him in finding the mean of 2450.

Factors of 2450 are 1, 2, 5, 7, 10, 14, 25, 35, 49, 50, 70, 98, 175, 245, 350, 490, 1225, 2450.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 2450 is 1 + 2 + 5 + 7 + 10 + 14 + 25 + 35 + 49 + 50 + 70 + 98 + 175 + 245 + 350 + 490 + 1225 + 2450 = 5301.
Hence, the mean of factors of 2450 is 5301 ÷ 18 = 294.50.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 2450? Help her in writing all the factors.

Positive factors are 1, 2, 5, 7, 10, 14, 25, 35, 49, 50, 70, 98, 175, 245, 350, 490, 1225, 2450.
Negative factors are -1, -2, -5, -7, -10, -14, -25, -35, -49, -50, -70, -98, -175, -245, -350, -490, -1225, -2450.

Joey wants to write all the prime factors of 2450 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 2450 are 2, 5, 5, 7, 7.
So in exponential form it can be written as 2 x 52 x 72.

Kevin has been asked to write 17 factor(s) of 2450. Can you predict the answer?

17 factor(s) of 2450 are 1, 2, 5, 7, 10, 14, 25, 35, 49, 50, 70, 98, 175, 245, 350, 490, 1225.

Sammy is puzzled while calculating the prime factors of 2450. Can you help him find them?

Factors of 2450 are 1, 2, 5, 7, 10, 14, 25, 35, 49, 50, 70, 98, 175, 245, 350, 490, 1225, 2450.
Prime factors of 2450 are 2, 5, 5, 7, 7

What is prime factorization of 2450?

Prime factorization of 2450 is 2 x 5 x 5 x 7 x 7 = 2 x 52 x 72.

Can you help Rubel to find out the product of the even factors of 2450?

Factors of 2450 are 1, 2, 5, 7, 10, 14, 25, 35, 49, 50, 70, 98, 175, 245, 350, 490, 1225, 2450.
Even factors of 2450 are 2, 10, 14, 50, 70, 98, 350, 490, 2450.
Hence, product of even factors of 2450 is; 2 x 10 x 14 x 50 x 70 x 98 x 350 x 490 x 2450 = 40353607000000000.