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Factors of 3500

Factors of 3500 are numbers that, when multiplied in pairs give the product as 3500. There are overall 24 factors of 3500, of which 2, 5, 7 are its prime factors. The sum of all factors of 3500 is 8736.

  • All Factors of 3500: 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 125, 140, 175, 250, 350, 500, 700, 875, 1750 and 3500
  • Prime Factors of 3500: 2, 5, 7
  • Prime Factorization of 3500: 22 × 53 × 71
  • Sum of Factors of 3500: 8736
1. What Are the Factors of 3500?
2. Factors of 3500 by Prime Factorization
3. Factors of 3500 in Pairs
4. FAQs on Factors of 3500
Factors of 3500

What are Factors of 3500?

Factors of 3500 are pairs of those numbers whose products result in 3500. These factors are either prime numbers or composite numbers.

How to Find the Factors of 3500?

To find the factors of 3500, we will have to find the list of numbers that would divide 3500 without leaving any remainder.

  • 3500/28 = 125; therefore, 28 is a factor of 3500 and 125 is also a factor of 3500.
  • 3500/10 = 350; therefore, 10 is a factor of 3500 and 350 is also a factor of 3500.
Similarly we can find other factors. Hence, the factors of 3500 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 125, 140, 175, 250, 350, 500, 700, 875, 1750, 3500.

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Factors of 3500 by Prime Factorization

The number 3500 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 3500. The first step is to divide the number 3500 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 3500 ÷ 2 = 1750
  • 1750 ÷ 2 = 875

Further dividing 875 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 875 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 3500 can be written as 22 × 53 × 71 where 2, 5, 7 are prime.

 

Factors of 3500 in Pairs

Pair factors of 3500 are the pairs of numbers that when multiplied give the product 3500. The factors of 3500 in pairs are:

  • 1 × 3500 = (1, 3500)
  • 2 × 1750 = (2, 1750)
  • 4 × 875 = (4, 875)
  • 5 × 700 = (5, 700)
  • 7 × 500 = (7, 500)
  • 10 × 350 = (10, 350)
  • 14 × 250 = (14, 250)
  • 20 × 175 = (20, 175)
  • 25 × 140 = (25, 140)
  • 28 × 125 = (28, 125)
  • 35 × 100 = (35, 100)
  • 50 × 70 = (50, 70)

Negative pair factors of 3500 are:

  • -1 × -3500 = (-1, -3500)
  • -2 × -1750 = (-2, -1750)
  • -4 × -875 = (-4, -875)
  • -5 × -700 = (-5, -700)
  • -7 × -500 = (-7, -500)
  • -10 × -350 = (-10, -350)
  • -14 × -250 = (-14, -250)
  • -20 × -175 = (-20, -175)
  • -25 × -140 = (-25, -140)
  • -28 × -125 = (-28, -125)
  • -35 × -100 = (-35, -100)
  • -50 × -70 = (-50, -70)

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

Factors of 3500 Solved Examples

  1. Example 1: How many factors are there for 3500?

    Solution:

    The factors of 3500 are too many, therefore if we can find the prime factorization of 3500, 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 3500 = 22 × 53 × 71
    Therefore, the total number of factors are (2 + 1) × (3 + 1) × (1 + 1) = 3 × 4 × 2 = 24

  2. Example 2: Find the Least Common Multiple and Greatest Common Factor (GCF) of 3500 and 415.

    Solution:

    The factors of 3500 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 125, 140, 175, 250, 350, 500, 700, 875, 1750, 3500 and factors of 415 are 1, 5, 83, 415.

    Therefore, the Least Common Multiple of 3500 and 415 is 290500 and Greatest Common Factor (GCF) of 3500 and 415 is 5.

  3. Example 3: Find if 1, 4, 5, 100, 250, 500, 936 and 1750 are factors of 3500.

    Solution:

    When we divide 3500 by 936 it leaves a remainder. Therefore, the number 936 is not a factor of 3500. All numbers except 936 are factors of 3500.

  4. Example 4: Find the product of all the prime factors of 3500.

    Solution:

    Since, the prime factors of 3500 are 2, 5, 7. Therefore, the product of prime factors = 2 × 5 × 7 = 70.

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FAQs on Factors of 3500

What are the Factors of 3500?

The factors of 3500 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 125, 140, 175, 250, 350, 500, 700, 875, 1750, 3500 and its negative factors are -1, -2, -4, -5, -7, -10, -14, -20, -25, -28, -35, -50, -70, -100, -125, -140, -175, -250, -350, -500, -700, -875, -1750, -3500.

What is the Sum of Factors of 3500?

Sum of all factors of 3500 = (22 + 1 - 1)/(2 - 1) × (53 + 1 - 1)/(5 - 1) × (71 + 1 - 1)/(7 - 1) = 8736

What Numbers are the Prime Factors of 3500?

The prime factors of 3500 are 2, 5, 7.

What is the Greatest Common Factor of 3500 and 954?

The factors of 3500 and 954 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 125, 140, 175, 250, 350, 500, 700, 875, 1750, 3500 and 1, 2, 3, 6, 9, 18, 53, 106, 159, 318, 477, 954 respectively.

Common factors of 3500 and 954 are [1, 2].

Hence, the GCF of 3500 and 954 is 2.

What are the Common Factors of 3500 and 3268?

Since, the factors of 3500 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 125, 140, 175, 250, 350, 500, 700, 875, 1750, 3500 and the factors of 3268 are 1, 2, 4, 19, 38, 43, 76, 86, 172, 817, 1634, 3268.
Hence, [1, 2, 4] are the common factors of 3500 and 3268.

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