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Factors of 1224

Factors of 1224 are numbers that, when multiplied in pairs give the product as 1224. There are overall 24 factors of 1224 among which 1224 is the biggest factor and 2, 3, 17 are its prime factors. The Prime Factorization of 1224 is 23 × 32 × 171.

  • All Factors of 1224: 1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 68, 72, 102, 136, 153, 204, 306, 408, 612 and 1224
  • Prime Factors of 1224: 2, 3, 17
  • Prime Factorization of 1224: 23 × 32 × 171
  • Sum of Factors of 1224: 3510
1. What Are the Factors of 1224?
2. Factors of 1224 by Prime Factorization
3. Factors of 1224 in Pairs
4. FAQs on Factors of 1224
Factors of 1224

What are Factors of 1224?

Factors of 1224 are pairs of those numbers whose products result in 1224. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1224?

To find the factors of 1224, we will have to find the list of numbers that would divide 1224 without leaving any remainder.

  • 1224/3 = 408; therefore, 3 is a factor of 1224 and 408 is also a factor of 1224.
  • 1224/102 = 12; therefore, 102 is a factor of 1224 and 12 is also a factor of 1224.
Similarly we can find other factors. Hence, the factors of 1224 are 1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 68, 72, 102, 136, 153, 204, 306, 408, 612, 1224.

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Factors of 1224 by Prime Factorization

The number 1224 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1224. The first step is to divide the number 1224 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 1224 ÷ 2 = 612
  • 612 ÷ 2 = 306
  • 306 ÷ 2 = 153

Further dividing 153 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 153 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 1224 can be written as 23 × 32 × 171 where 2, 3, 17 are prime.

 

Factors of 1224 in Pairs

Pair factors of 1224 are the pairs of numbers that when multiplied give the product 1224. The factors of 1224 in pairs are:

  • 1 × 1224 = (1, 1224)
  • 2 × 612 = (2, 612)
  • 3 × 408 = (3, 408)
  • 4 × 306 = (4, 306)
  • 6 × 204 = (6, 204)
  • 8 × 153 = (8, 153)
  • 9 × 136 = (9, 136)
  • 12 × 102 = (12, 102)
  • 17 × 72 = (17, 72)
  • 18 × 68 = (18, 68)
  • 24 × 51 = (24, 51)
  • 34 × 36 = (34, 36)

Negative pair factors of 1224 are:

  • -1 × -1224 = (-1, -1224)
  • -2 × -612 = (-2, -612)
  • -3 × -408 = (-3, -408)
  • -4 × -306 = (-4, -306)
  • -6 × -204 = (-6, -204)
  • -8 × -153 = (-8, -153)
  • -9 × -136 = (-9, -136)
  • -12 × -102 = (-12, -102)
  • -17 × -72 = (-17, -72)
  • -18 × -68 = (-18, -68)
  • -24 × -51 = (-24, -51)
  • -34 × -36 = (-34, -36)

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

Factors of 1224 Solved Examples

  1. Example 1: How many factors are there for 1224?

    Solution:

    The factors of 1224 are too many, therefore if we can find the prime factorization of 1224, 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 1224 = 23 × 32 × 171
    Therefore, the total number of factors are (3 + 1) × (2 + 1) × (1 + 1) = 4 × 3 × 2 = 24

  2. Example 2: Find the Least Common Multiple (LCM) and Greatest Common Factor (GCF) of 1224 and 411.

    Solution:

    The factors of 1224 are 1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 68, 72, 102, 136, 153, 204, 306, 408, 612, 1224 and factors of 411 are 1, 3, 137, 411.

    Therefore, the Least Common Multiple (LCM) of 1224 and 411 is 167688 and Greatest Common Factor (GCF) of 1224 and 411 is 3.

  3. Example 3: Find if 3, 6, 8, 12, 68, 141, 306 and 408 are factors of 1224.

    Solution:

    When we divide 1224 by 141 it leaves a remainder. Therefore, the number 141 is not a factor of 1224. All numbers except 141 are factors of 1224.

  4. Example 4: Find the product of all the prime factors of 1224.

    Solution:

    Since, the prime factors of 1224 are 2, 3, 17. Therefore, the product of prime factors = 2 × 3 × 17 = 102.

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FAQs on Factors of 1224

What are the Factors of 1224?

The factors of 1224 are 1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 68, 72, 102, 136, 153, 204, 306, 408, 612, 1224 and its negative factors are -1, -2, -3, -4, -6, -8, -9, -12, -17, -18, -24, -34, -36, -51, -68, -72, -102, -136, -153, -204, -306, -408, -612, -1224.

What is the Sum of the Factors of 1224?

Sum of all factors of 1224 = (23 + 1 - 1)/(2 - 1) × (32 + 1 - 1)/(3 - 1) × (171 + 1 - 1)/(17 - 1) = 3510

What Numbers are the Prime Factors of 1224?

The prime factors of 1224 are 2, 3, 17.

What is the Greatest Common Factor of 1224 and 101?

The factors of 1224 are 1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 68, 72, 102, 136, 153, 204, 306, 408, 612, 1224 and the factors of 101 are 1, 101. 1224 and 101 have only one common factor which is 1. This implies that 1224 and 101 are co-prime.

Hence, the Greatest Common Factor (GCF) of 1224 and 101 is 1.

How Many Factors of 1224 are also Factors of 201?

Since, the factors of 1224 are 1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 68, 72, 102, 136, 153, 204, 306, 408, 612, 1224 and the factors of 201 are 1, 3, 67, 201.
Hence, [1, 3] are the common factors of 1224 and 201.

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