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Factors of 416

Factors of 416 are the list of integers that can be evenly divided into 416. There are overall 12 factors of 416 among which 416 is the biggest factor and 2, 13 are its prime factors. The Prime Factorization of 416 is 25 × 131.

  • All Factors of 416: 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208 and 416
  • Prime Factors of 416: 2, 13
  • Prime Factorization of 416: 25 × 131
  • Sum of Factors of 416: 882
1. What Are the Factors of 416?
2. Factors of 416 by Prime Factorization
3. Factors of 416 in Pairs
4. FAQs on Factors of 416
Factors of 416

What are Factors of 416?

Factors of 416 are pairs of those numbers whose products result in 416. These factors are either prime numbers or composite numbers.

How to Find the Factors of 416?

To find the factors of 416, we will have to find the list of numbers that would divide 416 without leaving any remainder.

  • 416/2 = 208; therefore, 2 is a factor of 416 and 208 is also a factor of 416.
  • 416/8 = 52; therefore, 8 is a factor of 416 and 52 is also a factor of 416.
Similarly we can find other factors. Hence, the factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416.

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Factors of 416 by Prime Factorization

The number 416 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 416. The first step is to divide the number 416 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 416 ÷ 2 = 208
  • 208 ÷ 2 = 104
  • 104 ÷ 2 = 52
  • 52 ÷ 2 = 26
  • 26 ÷ 2 = 13

Further dividing 13 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 13 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 416 can be written as 25 × 131 where 2, 13 are prime.

 

Factors of 416 in Pairs

Pair factors of 416 are the pairs of numbers that when multiplied give the product 416. The factors of 416 in pairs are:

  • 1 × 416 = (1, 416)
  • 2 × 208 = (2, 208)
  • 4 × 104 = (4, 104)
  • 8 × 52 = (8, 52)
  • 13 × 32 = (13, 32)
  • 16 × 26 = (16, 26)

Negative pair factors of 416 are:

  • -1 × -416 = (-1, -416)
  • -2 × -208 = (-2, -208)
  • -4 × -104 = (-4, -104)
  • -8 × -52 = (-8, -52)
  • -13 × -32 = (-13, -32)
  • -16 × -26 = (-16, -26)

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

Factors of 416 Solved Examples

  1. Example 1: How many factors are there for 416?

    Solution:

    The factors of 416 are too many, therefore if we can find the prime factorization of 416, 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 416 = 25 × 131
    Therefore, the total number of factors are (5 + 1) × (1 + 1) = 6 × 2 = 12

  2. Example 2: Find the Least Common Multiple (LCM) and Greatest Common Divisor (GCD) of 416 and 59.

    Solution:

    The factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416 and factors of 59 are 1, 59.

    Therefore, the Least Common Multiple (LCM) of 416 and 59 is 24544 and Greatest Common Divisor (GCD) of 416 and 59 is 1.

  3. Example 3: Find if 1, 2, 13, 16, 26, 184 and 416 are factors of 416.

    Solution:

    When we divide 416 by 184 it leaves a remainder. Therefore, the number 184 is not a factor of 416. All numbers except 184 are factors of 416.

  4. Example 4: Find the product of all the prime factors of 416.

    Solution:

    Since, the prime factors of 416 are 2, 13. Therefore, the product of prime factors = 2 × 13 = 26.

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FAQs on Factors of 416

What are the Factors of 416?

The factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416 and its negative factors are -1, -2, -4, -8, -13, -16, -26, -32, -52, -104, -208, -416.

What is the Sum of the Factors of 416?

Sum of all factors of 416 = (25 + 1 - 1)/(2 - 1) × (131 + 1 - 1)/(13 - 1) = 882

What are Pair Factors of 416?

The pair factors of 416 are (1, 416), (2, 208), (4, 104), (8, 52), (13, 32), (16, 26).

What is the Greatest Common Factor of 416 and 141?

The factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416 and the factors of 141 are 1, 3, 47, 141. 416 and 141 have only one common factor which is 1. This implies that 416 and 141 are co-prime.

Hence, the Greatest Common Factor (GCF) of 416 and 141 is 1.

How Many Factors of 416 are also Factors of 347?

Since, the factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416 and factors of 347 are 1, 347. Hence, 416 and 347 have only one common factor which is 1. Therefore, 416 and 347 are co-prime.

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