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Factors of 700

Factors of 700 are numbers that, when multiplied in pairs give the product as 700. It has total 18 factors of which 700 is the biggest factor and the prime factors of 700 are 2, 5, 7. The sum of all factors of 700 is 1736.

  • All Factors of 700: 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350 and 700
  • Prime Factors of 700: 2, 5, 7
  • Prime Factorization of 700: 22 × 52 × 71
  • Sum of Factors of 700: 1736
1. What Are the Factors of 700?
2. Factors of 700 by Prime Factorization
3. Factors of 700 in Pairs
4. FAQs on Factors of 700
Factors of 700

What are Factors of 700?

Factors of 700 are pairs of those numbers whose products result in 700. These factors are either prime numbers or composite numbers.

How to Find the Factors of 700?

To find the factors of 700, we will have to find the list of numbers that would divide 700 without leaving any remainder.

  • 700/7 = 100; therefore, 7 is a factor of 700 and 100 is also a factor of 700.
  • 700/5 = 140; therefore, 5 is a factor of 700 and 140 is also a factor of 700.
Similarly we can find other factors. Hence, the factors of 700 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, 700.

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Factors of 700 by Prime Factorization

The number 700 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 700. The first step is to divide the number 700 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 700 ÷ 2 = 350
  • 350 ÷ 2 = 175

Further dividing 175 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 175 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 700 can be written as 22 × 52 × 71 where 2, 5, 7 are prime.

 

Factors of 700 in Pairs

Pair factors of 700 are the pairs of numbers that when multiplied give the product 700. The factors of 700 in pairs are:

  • 1 × 700 = (1, 700)
  • 2 × 350 = (2, 350)
  • 4 × 175 = (4, 175)
  • 5 × 140 = (5, 140)
  • 7 × 100 = (7, 100)
  • 10 × 70 = (10, 70)
  • 14 × 50 = (14, 50)
  • 20 × 35 = (20, 35)
  • 25 × 28 = (25, 28)

Negative pair factors of 700 are:

  • -1 × -700 = (-1, -700)
  • -2 × -350 = (-2, -350)
  • -4 × -175 = (-4, -175)
  • -5 × -140 = (-5, -140)
  • -7 × -100 = (-7, -100)
  • -10 × -70 = (-10, -70)
  • -14 × -50 = (-14, -50)
  • -20 × -35 = (-20, -35)
  • -25 × -28 = (-25, -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 700 Solved Examples

  1. Example 1: How many factors are there for 700?

    Solution:

    The factors of 700 are too many, therefore if we can find the prime factorization of 700, 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 700 = 22 × 52 × 71
    Therefore, the total number of factors are (2 + 1) × (2 + 1) × (1 + 1) = 3 × 3 × 2 = 18

  2. Example 2: Find the Lowest Common Multiple (LCM) and Highest Common Factor (HCF) of 700 and 538.

    Solution:

    The factors of 700 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, 700 and factors of 538 are 1, 2, 269, 538.

    Therefore, the Lowest Common Multiple (LCM) of 700 and 538 is 188300 and Highest Common Factor (HCF) of 700 and 538 is 2.

  3. Example 3: Find if 5, 7, 25, 28, 35, 84, 100 and 140 are factors of 700.

    Solution:

    When we divide 700 by 84 it leaves a remainder. Therefore, the number 84 is not a factor of 700. All numbers except 84 are factors of 700.

  4. Example 4: Find the product of all the prime factors of 700.

    Solution:

    Since, the prime factors of 700 are 2, 5, 7. Therefore, the product of prime factors = 2 × 5 × 7 = 70.

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FAQs on Factors of 700

What are the Factors of 700?

The factors of 700 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, 700 and its negative factors are -1, -2, -4, -5, -7, -10, -14, -20, -25, -28, -35, -50, -70, -100, -140, -175, -350, -700.

What is the Sum of Factors of 700?

Sum of all factors of 700 = (22 + 1 - 1)/(2 - 1) × (52 + 1 - 1)/(5 - 1) × (71 + 1 - 1)/(7 - 1) = 1736

What are the Pair Factors of 700?

The pair factors of 700 are (1, 700), (2, 350), (4, 175), (5, 140), (7, 100), (10, 70), (14, 50), (20, 35), (25, 28).

What is the Greatest Common Factor of 700 and 107?

The factors of 700 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, 700 and the factors of 107 are 1, 107. 700 and 107 have only one common factor which is 1. This implies that 700 and 107 are co-prime.

Hence, the Greatest Common Factor (GCF) of 700 and 107 is 1.

How Many Factors of 700 are also common to the Factors of 588?

Since, the factors of 700 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, 700 and the factors of 588 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 588.
Hence, [1, 2, 4, 7, 14, 28] are the common factors of 700 and 588.

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