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Factors of 2450

Factors of 2450 are the list of integers that we can split evenly into 2450. There are overall 18 factors of 2450 among which 2450 is the biggest factor and 2, 5, 7 are its prime factors. The sum of all factors of 2450 is 5301.

  • All Factors of 2450: 1, 2, 5, 7, 10, 14, 25, 35, 49, 50, 70, 98, 175, 245, 350, 490, 1225 and 2450
  • Prime Factors of 2450: 2, 5, 7
  • Prime Factorization of 2450: 21 × 52 × 72
  • Sum of Factors of 2450: 5301
1. What Are the Factors of 2450?
2. Factors of 2450 by Prime Factorization
3. Factors of 2450 in Pairs
4. FAQs on Factors of 2450
Factors of 2450

What are Factors of 2450?

Factors of 2450 are pairs of those numbers whose products result in 2450. These factors are either prime numbers or composite numbers.

How to Find the Factors of 2450?

To find the factors of 2450, we will have to find the list of numbers that would divide 2450 without leaving any remainder.

  • 2450/5 = 490; therefore, 5 is a factor of 2450 and 490 is also a factor of 2450.
  • 2450/245 = 10; therefore, 245 is a factor of 2450 and 10 is also a factor of 2450.
Similarly we can find other factors. Hence, the factors of 2450 are 1, 2, 5, 7, 10, 14, 25, 35, 49, 50, 70, 98, 175, 245, 350, 490, 1225, 2450.

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Factors of 2450 by Prime Factorization

The number 2450 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 2450. The first step is to divide the number 2450 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 2450 ÷ 2 = 1225

Further dividing 1225 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 1225 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 2450 can be written as 21 × 52 × 72 where 2, 5, 7 are prime.

 

Factors of 2450 in Pairs

Pair factors of 2450 are the pairs of numbers that when multiplied give the product 2450. The factors of 2450 in pairs are:

  • 1 × 2450 = (1, 2450)
  • 2 × 1225 = (2, 1225)
  • 5 × 490 = (5, 490)
  • 7 × 350 = (7, 350)
  • 10 × 245 = (10, 245)
  • 14 × 175 = (14, 175)
  • 25 × 98 = (25, 98)
  • 35 × 70 = (35, 70)
  • 49 × 50 = (49, 50)

Negative pair factors of 2450 are:

  • -1 × -2450 = (-1, -2450)
  • -2 × -1225 = (-2, -1225)
  • -5 × -490 = (-5, -490)
  • -7 × -350 = (-7, -350)
  • -10 × -245 = (-10, -245)
  • -14 × -175 = (-14, -175)
  • -25 × -98 = (-25, -98)
  • -35 × -70 = (-35, -70)
  • -49 × -50 = (-49, -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 2450 Solved Examples

  1. Example 1: How many factors are there for 2450?

    Solution:

    The factors of 2450 are too many, therefore if we can find the prime factorization of 2450, 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 2450 = 21 × 52 × 72
    Therefore, the total number of factors are (1 + 1) × (2 + 1) × (2 + 1) = 2 × 3 × 3 = 18

  2. Example 2: Find the Lowest Common Multiple (LCM) and Greatest Common Divisor (GCD) of 2450 and 280.

    Solution:

    The factors of 2450 are 1, 2, 5, 7, 10, 14, 25, 35, 49, 50, 70, 98, 175, 245, 350, 490, 1225, 2450 and factors of 280 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280.

    Therefore, the Lowest Common Multiple (LCM) of 2450 and 280 is 9800 and Greatest Common Divisor (GCD) of 2450 and 280 is 70.

  3. Example 3: Find if 1, 2, 5, 14, 245, 490, 928 and 1225 are factors of 2450.

    Solution:

    When we divide 2450 by 928 it leaves a remainder. Therefore, the number 928 is not a factor of 2450. All numbers except 928 are factors of 2450.

  4. Example 4: Find the product of all the prime factors of 2450.

    Solution:

    Since, the prime factors of 2450 are 2, 5, 7. Therefore, the product of prime factors = 2 × 5 × 7 = 70.

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FAQs on Factors of 2450

What are the Factors of 2450?

The factors of 2450 are 1, 2, 5, 7, 10, 14, 25, 35, 49, 50, 70, 98, 175, 245, 350, 490, 1225, 2450 and its negative factors are -1, -2, -5, -7, -10, -14, -25, -35, -49, -50, -70, -98, -175, -245, -350, -490, -1225, -2450.

What is the Sum of Factors of 2450?

Sum of all factors of 2450 = (21 + 1 - 1)/(2 - 1) × (52 + 1 - 1)/(5 - 1) × (72 + 1 - 1)/(7 - 1) = 5301

What are the Pair Factors of 2450?

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

What is the Greatest Common Factor of 2450 and 596?

The factors of 2450 and 596 are 1, 2, 5, 7, 10, 14, 25, 35, 49, 50, 70, 98, 175, 245, 350, 490, 1225, 2450 and 1, 2, 4, 149, 298, 596 respectively.

Common factors of 2450 and 596 are [1, 2].

Hence, the GCF of 2450 and 596 is 2.

How Many Factors of 2450 are also Factors of 770?

Since, the factors of 2450 are 1, 2, 5, 7, 10, 14, 25, 35, 49, 50, 70, 98, 175, 245, 350, 490, 1225, 2450 and the factors of 770 are 1, 2, 5, 7, 10, 11, 14, 22, 35, 55, 70, 77, 110, 154, 385, 770.
Hence, [1, 2, 5, 7, 10, 14, 35, 70] are the common factors of 2450 and 770.

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