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Factors of 476

Factors of 476 are the list of integers that we can split evenly into 476. There are overall 12 factors of 476 among which 476 is the biggest factor and its prime factors are 2, 7, 17. The Prime Factorization of 476 is 22 × 71 × 171.

  • All Factors of 476: 1, 2, 4, 7, 14, 17, 28, 34, 68, 119, 238 and 476
  • Prime Factors of 476: 2, 7, 17
  • Prime Factorization of 476: 22 × 71 × 171
  • Sum of Factors of 476: 1008
1. What Are the Factors of 476?
2. Factors of 476 by Prime Factorization
3. Factors of 476 in Pairs
4. FAQs on Factors of 476
Factors of 476

What are Factors of 476?

Factors of 476 are pairs of those numbers whose products result in 476. These factors are either prime numbers or composite numbers.

How to Find the Factors of 476?

To find the factors of 476, we will have to find the list of numbers that would divide 476 without leaving any remainder.

  • 476/28 = 17; therefore, 28 is a factor of 476 and 17 is also a factor of 476.
  • 476/7 = 68; therefore, 7 is a factor of 476 and 68 is also a factor of 476.
Similarly we can find other factors. Hence, the factors of 476 are 1, 2, 4, 7, 14, 17, 28, 34, 68, 119, 238, 476.

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Factors of 476 by Prime Factorization

The number 476 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 476. The first step is to divide the number 476 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 476 ÷ 2 = 238
  • 238 ÷ 2 = 119

Further dividing 119 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 119 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 476 can be written as 22 × 71 × 171 where 2, 7, 17 are prime.

 

Factors of 476 in Pairs

Pair factors of 476 are the pairs of numbers that when multiplied give the product 476. The factors of 476 in pairs are:

  • 1 × 476 = (1, 476)
  • 2 × 238 = (2, 238)
  • 4 × 119 = (4, 119)
  • 7 × 68 = (7, 68)
  • 14 × 34 = (14, 34)
  • 17 × 28 = (17, 28)

Negative pair factors of 476 are:

  • -1 × -476 = (-1, -476)
  • -2 × -238 = (-2, -238)
  • -4 × -119 = (-4, -119)
  • -7 × -68 = (-7, -68)
  • -14 × -34 = (-14, -34)
  • -17 × -28 = (-17, -28)

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

Factors of 476 Solved Examples

  1. Example 1: How many factors are there for 476?

    Solution:

    The factors of 476 are too many, therefore if we can find the prime factorization of 476, 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 476 = 22 × 71 × 171
    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 Greatest Common Divisor (GCD) of 476 and 290.

    Solution:

    The factors of 476 are 1, 2, 4, 7, 14, 17, 28, 34, 68, 119, 238, 476 and factors of 290 are 1, 2, 5, 10, 29, 58, 145, 290.

    Therefore, the Lowest Common Multiple (LCM) of 476 and 290 is 69020 and Greatest Common Divisor (GCD) of 476 and 290 is 2.

  3. Example 3: Find if 2, 34, 68, 119, 138, 238 and 476 are factors of 476.

    Solution:

    When we divide 476 by 138 it leaves a remainder. Therefore, the number 138 is not a factor of 476. All numbers except 138 are factors of 476.

  4. Example 4: Find the product of all the prime factors of 476.

    Solution:

    Since, the prime factors of 476 are 2, 7, 17. Therefore, the product of prime factors = 2 × 7 × 17 = 238.

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FAQs on Factors of 476

What are the Factors of 476?

The factors of 476 are 1, 2, 4, 7, 14, 17, 28, 34, 68, 119, 238, 476 and its negative factors are -1, -2, -4, -7, -14, -17, -28, -34, -68, -119, -238, -476.

What is the Sum of the Factors of 476?

Sum of all factors of 476 = (22 + 1 - 1)/(2 - 1) × (71 + 1 - 1)/(7 - 1) × (171 + 1 - 1)/(17 - 1) = 1008

What are Prime Factors of 476?

The prime factors of 476 are 2, 7, 17.

What is the Greatest Common Factor of 476 and 27?

The factors of 476 are 1, 2, 4, 7, 14, 17, 28, 34, 68, 119, 238, 476 and the factors of 27 are 1, 3, 9, 27. 476 and 27 have only one common factor which is 1. This implies that 476 and 27 are co-prime.

Hence, the Greatest Common Factor (GCF) of 476 and 27 is 1.

How Many Factors of 476 are also Factors of 270?

Since, the factors of 476 are 1, 2, 4, 7, 14, 17, 28, 34, 68, 119, 238, 476 and the factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270.
Hence, [1, 2] are the common factors of 476 and 270.

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