A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
LearnPracticeDownload

 

Factors of 1050

Factors of 1050 are the list of integers that can be evenly divided into 1050. There are total 24 factors of 1050, of which 2, 3, 5, 7 are its prime factors. The sum of all factors of 1050 is 2976.

  • All Factors of 1050: 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 25, 30, 35, 42, 50, 70, 75, 105, 150, 175, 210, 350, 525 and 1050
  • Prime Factors of 1050: 2, 3, 5, 7
  • Prime Factorization of 1050: 21 × 31 × 52 × 71
  • Sum of Factors of 1050: 2976
1. What Are the Factors of 1050?
2. Factors of 1050 by Prime Factorization
3. Factors of 1050 in Pairs
4. FAQs on Factors of 1050
Factors of 1050

What are Factors of 1050?

Factors of 1050 are pairs of those numbers whose products result in 1050. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1050?

To find the factors of 1050, we will have to find the list of numbers that would divide 1050 without leaving any remainder.

  • 1050/70 = 15; therefore, 70 is a factor of 1050 and 15 is also a factor of 1050.
  • 1050/50 = 21; therefore, 50 is a factor of 1050 and 21 is also a factor of 1050.
Similarly we can find other factors. Hence, the factors of 1050 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 25, 30, 35, 42, 50, 70, 75, 105, 150, 175, 210, 350, 525, 1050.

☛ Also Check:

Factors of 1050 by Prime Factorization

The number 1050 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1050. The first step is to divide the number 1050 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 1050 ÷ 2 = 525

Further dividing 525 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 525 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 1050 can be written as 21 × 31 × 52 × 71 where 2, 3, 5, 7 are prime.

 

Factors of 1050 in Pairs

Pair factors of 1050 are the pairs of numbers that when multiplied give the product 1050. The factors of 1050 in pairs are:

  • 1 × 1050 = (1, 1050)
  • 2 × 525 = (2, 525)
  • 3 × 350 = (3, 350)
  • 5 × 210 = (5, 210)
  • 6 × 175 = (6, 175)
  • 7 × 150 = (7, 150)
  • 10 × 105 = (10, 105)
  • 14 × 75 = (14, 75)
  • 15 × 70 = (15, 70)
  • 21 × 50 = (21, 50)
  • 25 × 42 = (25, 42)
  • 30 × 35 = (30, 35)

Negative pair factors of 1050 are:

  • -1 × -1050 = (-1, -1050)
  • -2 × -525 = (-2, -525)
  • -3 × -350 = (-3, -350)
  • -5 × -210 = (-5, -210)
  • -6 × -175 = (-6, -175)
  • -7 × -150 = (-7, -150)
  • -10 × -105 = (-10, -105)
  • -14 × -75 = (-14, -75)
  • -15 × -70 = (-15, -70)
  • -21 × -50 = (-21, -50)
  • -25 × -42 = (-25, -42)
  • -30 × -35 = (-30, -35)

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

Factors of 1050 Solved Examples

  1. Example 1: How many factors are there for 1050?

    Solution:

    The factors of 1050 are too many, therefore if we can find the prime factorization of 1050, 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 1050 = 21 × 31 × 52 × 71
    Therefore, the total number of factors are (1 + 1) × (1 + 1) × (2 + 1) × (1 + 1) = 2 × 2 × 3 × 2 = 24

  2. Example 2: Find the Least Common Multiple and Highest Common Factor (HCF) of 1050 and 440.

    Solution:

    The factors of 1050 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 25, 30, 35, 42, 50, 70, 75, 105, 150, 175, 210, 350, 525, 1050 and factors of 440 are 1, 2, 4, 5, 8, 10, 11, 20, 22, 40, 44, 55, 88, 110, 220, 440.

    Therefore, the Least Common Multiple of 1050 and 440 is 46200 and Highest Common Factor (HCF) of 1050 and 440 is 10.

  3. Example 3: Find if 21, 42, 50, 70, 75, 210, 358 and 1050 are factors of 1050.

    Solution:

    When we divide 1050 by 358 it leaves a remainder. Therefore, the number 358 is not a factor of 1050. All numbers except 358 are factors of 1050.

  4. Example 4: Find the product of all the prime factors of 1050.

    Solution:

    Since, the prime factors of 1050 are 2, 3, 5, 7. Therefore, the product of prime factors = 2 × 3 × 5 × 7 = 210.

Show Solution >

go to slidego to slidego to slidego to slide

 

Ready to see the world through math’s eyes?
Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything. 

Book a Free Trial Class

 

FAQs on Factors of 1050

What are the Factors of 1050?

The factors of 1050 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 25, 30, 35, 42, 50, 70, 75, 105, 150, 175, 210, 350, 525, 1050 and its negative factors are -1, -2, -3, -5, -6, -7, -10, -14, -15, -21, -25, -30, -35, -42, -50, -70, -75, -105, -150, -175, -210, -350, -525, -1050.

What is the Sum of the Factors of 1050?

Sum of all factors of 1050 = (21 + 1 - 1)/(2 - 1) × (31 + 1 - 1)/(3 - 1) × (52 + 1 - 1)/(5 - 1) × (71 + 1 - 1)/(7 - 1) = 2976

What are the Prime Factors of 1050?

The prime factors of 1050 are 2, 3, 5, 7.

What is the Greatest Common Factor of 1050 and 256?

The factors of 1050 and 256 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 25, 30, 35, 42, 50, 70, 75, 105, 150, 175, 210, 350, 525, 1050 and 1, 2, 4, 8, 16, 32, 64, 128, 256 respectively.

Common factors of 1050 and 256 are [1, 2].

Hence, the Greatest Common Factor of 1050 and 256 is 2.

How Many Factors of 310 are also common to the Factors of 1050?

Since, the factors of 1050 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 25, 30, 35, 42, 50, 70, 75, 105, 150, 175, 210, 350, 525, 1050 and the factors of 310 are 1, 2, 5, 10, 31, 62, 155, 310.
Hence, [1, 2, 5, 10] are the common factors of 1050 and 310.

Math worksheets and
visual curriculum