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Factors of 714

Factors of 714 are the list of integers that we can split evenly into 714. There are overall 16 factors of 714 among which 714 is the biggest factor and its prime factors are 2, 3, 7, 17. The Prime Factorization of 714 is 21 × 31 × 71 × 171.

  • All Factors of 714: 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357 and 714
  • Prime Factors of 714: 2, 3, 7, 17
  • Prime Factorization of 714: 21 × 31 × 71 × 171
  • Sum of Factors of 714: 1728
1. What Are the Factors of 714?
2. Factors of 714 by Prime Factorization
3. Factors of 714 in Pairs
4. FAQs on Factors of 714
Factors of 714

What are Factors of 714?

Factors of 714 are pairs of those numbers whose products result in 714. These factors are either prime numbers or composite numbers.

How to Find the Factors of 714?

To find the factors of 714, we will have to find the list of numbers that would divide 714 without leaving any remainder.

  • 714/17 = 42; therefore, 17 is a factor of 714 and 42 is also a factor of 714.
  • 714/102 = 7; therefore, 102 is a factor of 714 and 7 is also a factor of 714.
Similarly we can find other factors. Hence, the factors of 714 are 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714.

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Factors of 714 by Prime Factorization

The number 714 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 714. The first step is to divide the number 714 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 714 ÷ 2 = 357

Further dividing 357 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 357 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 714 can be written as 21 × 31 × 71 × 171 where 2, 3, 7, 17 are prime.

 

Factors of 714 in Pairs

Pair factors of 714 are the pairs of numbers that when multiplied give the product 714. The factors of 714 in pairs are:

  • 1 × 714 = (1, 714)
  • 2 × 357 = (2, 357)
  • 3 × 238 = (3, 238)
  • 6 × 119 = (6, 119)
  • 7 × 102 = (7, 102)
  • 14 × 51 = (14, 51)
  • 17 × 42 = (17, 42)
  • 21 × 34 = (21, 34)

Negative pair factors of 714 are:

  • -1 × -714 = (-1, -714)
  • -2 × -357 = (-2, -357)
  • -3 × -238 = (-3, -238)
  • -6 × -119 = (-6, -119)
  • -7 × -102 = (-7, -102)
  • -14 × -51 = (-14, -51)
  • -17 × -42 = (-17, -42)
  • -21 × -34 = (-21, -34)

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

Factors of 714 Solved Examples

  1. Example 1: How many factors are there for 714?

    Solution:

    The factors of 714 are too many, therefore if we can find the prime factorization of 714, 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 714 = 21 × 31 × 71 × 171
    Therefore, the total number of factors are (1 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 2 × 2 × 2 × 2 = 16

  2. Example 2: Find the Lowest Common Multiple (LCM) and Highest Common Factor (HCF) of 714 and 105.

    Solution:

    The factors of 714 are 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714 and factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105.

    Therefore, the Lowest Common Multiple (LCM) of 714 and 105 is 3570 and Highest Common Factor (HCF) of 714 and 105 is 21.

  3. Example 3: Find if 2, 14, 21, 42, 102, 238, 264 and 714 are factors of 714.

    Solution:

    When we divide 714 by 264 it leaves a remainder. Therefore, the number 264 is not a factor of 714. All numbers except 264 are factors of 714.

  4. Example 4: Find the product of all the prime factors of 714.

    Solution:

    Since, the prime factors of 714 are 2, 3, 7, 17. Therefore, the product of prime factors = 2 × 3 × 7 × 17 = 714.

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FAQs on Factors of 714

What are the Factors of 714?

The factors of 714 are 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714 and its negative factors are -1, -2, -3, -6, -7, -14, -17, -21, -34, -42, -51, -102, -119, -238, -357, -714.

What is the Sum of all the Factors of 714?

Sum of all factors of 714 = (21 + 1 - 1)/(2 - 1) × (31 + 1 - 1)/(3 - 1) × (71 + 1 - 1)/(7 - 1) × (171 + 1 - 1)/(17 - 1) = 1728

What are the Pair Factors of 714?

The pair factors of 714 are (1, 714), (2, 357), (3, 238), (6, 119), (7, 102), (14, 51), (17, 42), (21, 34).

What is the Greatest Common Factor of 714 and 269?

The factors of 714 are 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714 and the factors of 269 are 1, 269. 714 and 269 have only one common factor which is 1. This implies that 714 and 269 are co-prime.

Hence, the Greatest Common Factor (GCF) of 714 and 269 is 1.

How Many Factors of 714 are also common to the Factors of 204?

Since, the factors of 714 are 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714 and the factors of 204 are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204.
Hence, [1, 2, 3, 6, 17, 34, 51, 102] are the common factors of 714 and 204.

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