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Factors of 3136

Factors of 3136 are the list of integers that we can split evenly into 3136. It has total 21 factors of which 3136 is the biggest factor and the prime factors of 3136 are 2, 7. The Prime Factorization of 3136 is 26 × 72.

  • All Factors of 3136: 1, 2, 4, 7, 8, 14, 16, 28, 32, 49, 56, 64, 98, 112, 196, 224, 392, 448, 784, 1568 and 3136
  • Prime Factors of 3136: 2, 7
  • Prime Factorization of 3136: 26 × 72
  • Sum of Factors of 3136: 7239
1. What Are the Factors of 3136?
2. Factors of 3136 by Prime Factorization
3. Factors of 3136 in Pairs
4. FAQs on Factors of 3136
Factors of 3136

What are Factors of 3136?

Factors of 3136 are pairs of those numbers whose products result in 3136. These factors are either prime numbers or composite numbers.

How to Find the Factors of 3136?

To find the factors of 3136, we will have to find the list of numbers that would divide 3136 without leaving any remainder.

  • 3136/4 = 784; therefore, 4 is a factor of 3136 and 784 is also a factor of 3136.
  • 3136/112 = 28; therefore, 112 is a factor of 3136 and 28 is also a factor of 3136.
Similarly we can find other factors. Hence, the factors of 3136 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 49, 56, 64, 98, 112, 196, 224, 392, 448, 784, 1568, 3136.

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Factors of 3136 by Prime Factorization

The number 3136 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 3136. The first step is to divide the number 3136 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 3136 ÷ 2 = 1568
  • 1568 ÷ 2 = 784
  • 784 ÷ 2 = 392
  • 392 ÷ 2 = 196
  • 196 ÷ 2 = 98
  • 98 ÷ 2 = 49

Further dividing 49 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 49 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 3136 can be written as 26 × 72 where 2, 7 are prime.

 

Factors of 3136 in Pairs

Pair factors of 3136 are the pairs of numbers that when multiplied give the product 3136. The factors of 3136 in pairs are:

  • 1 × 3136 = (1, 3136)
  • 2 × 1568 = (2, 1568)
  • 4 × 784 = (4, 784)
  • 7 × 448 = (7, 448)
  • 8 × 392 = (8, 392)
  • 14 × 224 = (14, 224)
  • 16 × 196 = (16, 196)
  • 28 × 112 = (28, 112)
  • 32 × 98 = (32, 98)
  • 49 × 64 = (49, 64)
  • 56 × 56 = (56, 56)

Negative pair factors of 3136 are:

  • -1 × -3136 = (-1, -3136)
  • -2 × -1568 = (-2, -1568)
  • -4 × -784 = (-4, -784)
  • -7 × -448 = (-7, -448)
  • -8 × -392 = (-8, -392)
  • -14 × -224 = (-14, -224)
  • -16 × -196 = (-16, -196)
  • -28 × -112 = (-28, -112)
  • -32 × -98 = (-32, -98)
  • -49 × -64 = (-49, -64)
  • -56 × -56 = (-56, -56)

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

Factors of 3136 Solved Examples

  1. Example 1: How many factors are there for 3136?

    Solution:

    The factors of 3136 are too many, therefore if we can find the prime factorization of 3136, 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 3136 = 26 × 72
    Therefore, the total number of factors are (6 + 1) × (2 + 1) = 7 × 3 = 21

  2. Example 2: Find the Least Common Multiple (LCM) and Greatest Common Divisor (GCD) of 3136 and 190.

    Solution:

    The factors of 3136 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 49, 56, 64, 98, 112, 196, 224, 392, 448, 784, 1568, 3136 and factors of 190 are 1, 2, 5, 10, 19, 38, 95, 190.

    Therefore, the Least Common Multiple (LCM) of 3136 and 190 is 297920 and Greatest Common Divisor (GCD) of 3136 and 190 is 2.

  3. Example 3: Find if 1, 7, 8, 32, 196, 448, 1568 and 1793 are factors of 3136.

    Solution:

    When we divide 3136 by 1793 it leaves a remainder. Therefore, the number 1793 is not a factor of 3136. All numbers except 1793 are factors of 3136.

  4. Example 4: Find the product of all the prime factors of 3136.

    Solution:

    Since, the prime factors of 3136 are 2, 7. Therefore, the product of prime factors = 2 × 7 = 14.

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FAQs on Factors of 3136

What are the Factors of 3136?

The factors of 3136 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 49, 56, 64, 98, 112, 196, 224, 392, 448, 784, 1568, 3136 and its negative factors are -1, -2, -4, -7, -8, -14, -16, -28, -32, -49, -56, -64, -98, -112, -196, -224, -392, -448, -784, -1568, -3136.

What is the Sum of the Factors of 3136?

Sum of all factors of 3136 = (26 + 1 - 1)/(2 - 1) × (72 + 1 - 1)/(7 - 1) = 7239

What Numbers are the Prime Factors of 3136?

The prime factors of 3136 are 2, 7.

What is the Greatest Common Factor of 3136 and 125?

The factors of 3136 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 49, 56, 64, 98, 112, 196, 224, 392, 448, 784, 1568, 3136 and the factors of 125 are 1, 5, 25, 125. 3136 and 125 have only one common factor which is 1. This implies that 3136 and 125 are co-prime.

Hence, the Greatest Common Factor (GCF) of 3136 and 125 is 1.

What are the Common Factors of 3136 and 2835?

Since, the factors of 3136 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 49, 56, 64, 98, 112, 196, 224, 392, 448, 784, 1568, 3136 and the factors of 2835 are 1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 81, 105, 135, 189, 315, 405, 567, 945, 2835.
Hence, [1, 7] are the common factors of 3136 and 2835.

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