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Factors of 2170

Factors of 2170 are the list of integers that can be evenly divided into 2170. There are overall 16 factors of 2170, of which 2, 5, 7, 31 are its prime factors. The Prime Factorization of 2170 is 21 × 51 × 71 × 311.

  • All Factors of 2170: 1, 2, 5, 7, 10, 14, 31, 35, 62, 70, 155, 217, 310, 434, 1085 and 2170
  • Prime Factors of 2170: 2, 5, 7, 31
  • Prime Factorization of 2170: 21 × 51 × 71 × 311
  • Sum of Factors of 2170: 4608
1. What Are the Factors of 2170?
2. Factors of 2170 by Prime Factorization
3. Factors of 2170 in Pairs
4. FAQs on Factors of 2170
Factors of 2170

What are Factors of 2170?

Factors of 2170 are pairs of those numbers whose products result in 2170. These factors are either prime numbers or composite numbers.

How to Find the Factors of 2170?

To find the factors of 2170, we will have to find the list of numbers that would divide 2170 without leaving any remainder.

  • 2170/14 = 155; therefore, 14 is a factor of 2170 and 155 is also a factor of 2170.
  • 2170/70 = 31; therefore, 70 is a factor of 2170 and 31 is also a factor of 2170.
Similarly we can find other factors. Hence, the factors of 2170 are 1, 2, 5, 7, 10, 14, 31, 35, 62, 70, 155, 217, 310, 434, 1085, 2170.

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Factors of 2170 by Prime Factorization

The number 2170 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 2170. The first step is to divide the number 2170 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 2170 ÷ 2 = 1085

Further dividing 1085 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 1085 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 2170 can be written as 21 × 51 × 71 × 311 where 2, 5, 7, 31 are prime.

 

Factors of 2170 in Pairs

Pair factors of 2170 are the pairs of numbers that when multiplied give the product 2170. The factors of 2170 in pairs are:

  • 1 × 2170 = (1, 2170)
  • 2 × 1085 = (2, 1085)
  • 5 × 434 = (5, 434)
  • 7 × 310 = (7, 310)
  • 10 × 217 = (10, 217)
  • 14 × 155 = (14, 155)
  • 31 × 70 = (31, 70)
  • 35 × 62 = (35, 62)

Negative pair factors of 2170 are:

  • -1 × -2170 = (-1, -2170)
  • -2 × -1085 = (-2, -1085)
  • -5 × -434 = (-5, -434)
  • -7 × -310 = (-7, -310)
  • -10 × -217 = (-10, -217)
  • -14 × -155 = (-14, -155)
  • -31 × -70 = (-31, -70)
  • -35 × -62 = (-35, -62)

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

Factors of 2170 Solved Examples

  1. Example 1: How many factors are there for 2170?

    Solution:

    The factors of 2170 are too many, therefore if we can find the prime factorization of 2170, 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 2170 = 21 × 51 × 71 × 311
    Therefore, the total number of factors are (1 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 2 × 2 × 2 × 2 = 16

  2. Example 2: Find the Least Common Multiple (LCM) and Greatest Common Divisor (GCD) of 2170 and 855.

    Solution:

    The factors of 2170 are 1, 2, 5, 7, 10, 14, 31, 35, 62, 70, 155, 217, 310, 434, 1085, 2170 and factors of 855 are 1, 3, 5, 9, 15, 19, 45, 57, 95, 171, 285, 855.

    Therefore, the Least Common Multiple (LCM) of 2170 and 855 is 371070 and Greatest Common Divisor (GCD) of 2170 and 855 is 5.

  3. Example 3: Find if 1, 5, 62, 310, 434, 1085, 2026 and 2170 are factors of 2170.

    Solution:

    When we divide 2170 by 2026 it leaves a remainder. Therefore, the number 2026 is not a factor of 2170. All numbers except 2026 are factors of 2170.

  4. Example 4: Find the product of all the prime factors of 2170.

    Solution:

    Since, the prime factors of 2170 are 2, 5, 7, 31. Therefore, the product of prime factors = 2 × 5 × 7 × 31 = 2170.

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FAQs on Factors of 2170

What are the Factors of 2170?

The factors of 2170 are 1, 2, 5, 7, 10, 14, 31, 35, 62, 70, 155, 217, 310, 434, 1085, 2170 and its negative factors are -1, -2, -5, -7, -10, -14, -31, -35, -62, -70, -155, -217, -310, -434, -1085, -2170.

What is the Sum of all the Factors of 2170?

Sum of all factors of 2170 = (21 + 1 - 1)/(2 - 1) × (51 + 1 - 1)/(5 - 1) × (71 + 1 - 1)/(7 - 1) × (311 + 1 - 1)/(31 - 1) = 4608

What are the Pair Factors of 2170?

The pair factors of 2170 are (1, 2170), (2, 1085), (5, 434), (7, 310), (10, 217), (14, 155), (31, 70), (35, 62).

What is the Greatest Common Factor of 2170 and 589?

The factors of 2170 and 589 are 1, 2, 5, 7, 10, 14, 31, 35, 62, 70, 155, 217, 310, 434, 1085, 2170 and 1, 19, 31, 589 respectively.

Common factors of 2170 and 589 are [1, 31].

Hence, the Greatest Common Factor (GCF) of 2170 and 589 is 31.

How Many Factors of 2170 are also Factors of 680?

Since, the factors of 2170 are 1, 2, 5, 7, 10, 14, 31, 35, 62, 70, 155, 217, 310, 434, 1085, 2170 and the factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680.
Hence, [1, 2, 5, 10] are the common factors of 2170 and 680.

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