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Factors of 868

Factors of 868 are integers that can be divided evenly into 868. There are 12 factors of 868 of which 868 itself is the biggest factor and its prime factors are 2, 7, 31 The sum of all factors of 868 is 1792.

  • All Factors of 868: 1, 2, 4, 7, 14, 28, 31, 62, 124, 217, 434 and 868
  • Prime Factors of 868: 2, 7, 31
  • Prime Factorization of 868: 22 × 71 × 311
  • Sum of Factors of 868: 1792
1. What Are the Factors of 868?
2. Factors of 868 by Prime Factorization
3. Factors of 868 in Pairs
4. FAQs on Factors of 868
Factors of 868

What are Factors of 868?

Factors of 868 are pairs of those numbers whose products result in 868. These factors are either prime numbers or composite numbers.

How to Find the Factors of 868?

To find the factors of 868, we will have to find the list of numbers that would divide 868 without leaving any remainder.

  • 868/1 = 868; therefore, 1 is a factor of 868.
  • 868/124 = 7; therefore, 124 is a factor of 868.
Similarly we can find other factors. Hence, the factors of 868 are 1, 2, 4, 7, 14, 28, 31, 62, 124, 217, 434, 868.

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Factors of 868 by Prime Factorization

The number 868 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 868. The first step is to divide the number 868 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 868 ÷ 2 = 434
  • 434 ÷ 2 = 217

Further dividing 217 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 217 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 868 can be written as 22 × 71 × 311 where 2, 7, 31 are prime.

 

Factors of 868 in Pairs

Pair factors of 868 are the pairs of numbers that when multiplied give the product 868. The factors of 868 in pairs are:

  • 1 × 868 = (1, 868)
  • 2 × 434 = (2, 434)
  • 4 × 217 = (4, 217)
  • 7 × 124 = (7, 124)
  • 14 × 62 = (14, 62)
  • 28 × 31 = (28, 31)

Negative pair factors of 868 are:

  • -1 × -868 = (-1, -868)
  • -2 × -434 = (-2, -434)
  • -4 × -217 = (-4, -217)
  • -7 × -124 = (-7, -124)
  • -14 × -62 = (-14, -62)
  • -28 × -31 = (-28, -31)

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

Factors of 868 Solved Examples

  1. Example 1: How many factors are there for 868?

    Solution:

    The factors of 868 are too many, therefore if we can find the prime factorization of 868, 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 868 = 22 × 71 × 311
    Therefore, the total number of factors are (2 + 1) × (1 + 1) × (1 + 1) = 3 × 2 × 2 = 12

  2. Example 2: Find the Lowest Common Multiple (LCM) and Highest Common Factor (HCF) of 868 and 410.

    Solution:

    The factors of 868 are 1, 2, 4, 7, 14, 28, 31, 62, 124, 217, 434, 868 and factors of 410 are 1, 2, 5, 10, 41, 82, 205, 410.

    Therefore, the Lowest Common Multiple (LCM) of 868 and 410 is 177940 and Highest Common Factor (HCF) of 868 and 410 is 2.

  3. Example 3: Find if 2, 4, 14, 31, 62, 438 and 868 are factors of 868.

    Solution:

    When we divide 868 by 438 it leaves a remainder. Therefore, the number 438 is not a factor of 868. All numbers except 438 are factors of 868.

  4. Example 4: Find the product of all the prime factors of 868.

    Solution:

    Since, the prime factors of 868 are 2, 7, 31. Therefore, the product of prime factors = 2 × 7 × 31 = 434.

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FAQs on Factors of 868

What are the Factors of 868?

The factors of 868 are 1, 2, 4, 7, 14, 28, 31, 62, 124, 217, 434, 868 and its negative factors are -1, -2, -4, -7, -14, -28, -31, -62, -124, -217, -434, -868.

What is the Sum of Factors of 868?

Sum of all factors of 868 = (22 + 1 - 1)/(2 - 1) × (71 + 1 - 1)/(7 - 1) × (311 + 1 - 1)/(31 - 1) = 1792

What are the Prime Factors of 868?

The prime factors of 868 are 2, 7, 31.

What is the Greatest Common Factor of 868 and 245?

The factors of 868 and 245 are 1, 2, 4, 7, 14, 28, 31, 62, 124, 217, 434, 868 and 1, 5, 7, 35, 49, 245 respectively.

Common factors of 868 and 245 are [1, 7].

Hence, the GCF of 868 and 245 is 7.

How Many Factors of 868 are also common to the Factors of 526?

Since, the factors of 868 are 1, 2, 4, 7, 14, 28, 31, 62, 124, 217, 434, 868 and the factors of 526 are 1, 2, 263, 526.
Hence, [1, 2] are the common factors of 868 and 526.

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