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Factors of 1995

Factors of 1995 are numbers that, when multiplied in pairs give the product as 1995. There are overall 16 factors of 1995 among which 1995 is the biggest factor and 3, 5, 7, 19 are its prime factors. The Prime Factorization of 1995 is 31 × 51 × 71 × 191.

  • All Factors of 1995: 1, 3, 5, 7, 15, 19, 21, 35, 57, 95, 105, 133, 285, 399, 665 and 1995
  • Prime Factors of 1995: 3, 5, 7, 19
  • Prime Factorization of 1995: 31 × 51 × 71 × 191
  • Sum of Factors of 1995: 3840
1. What Are the Factors of 1995?
2. Factors of 1995 by Prime Factorization
3. Factors of 1995 in Pairs
4. FAQs on Factors of 1995
Factors of 1995

What are Factors of 1995?

Factors of 1995 are pairs of those numbers whose products result in 1995. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1995?

To find the factors of 1995, we will have to find the list of numbers that would divide 1995 without leaving any remainder.

  • 1995/5 = 399; therefore, 5 is a factor of 1995 and 399 is also a factor of 1995.
  • 1995/21 = 95; therefore, 21 is a factor of 1995 and 95 is also a factor of 1995.
Similarly we can find other factors. Hence, the factors of 1995 are 1, 3, 5, 7, 15, 19, 21, 35, 57, 95, 105, 133, 285, 399, 665, 1995.

☛ Also Check:

Factors of 1995 by Prime Factorization

The number 1995 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1995. The first step is to divide the number 1995 with the smallest prime factor, here it is 3. We keep dividing until it gives a non-zero remainder.
  • 1995 ÷ 3 = 665

Further dividing 665 by 3 gives a non-zero remainder. So we stop the process and continue dividing the number 665 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 1995 can be written as 31 × 51 × 71 × 191 where 3, 5, 7, 19 are prime.

 

Factors of 1995 in Pairs

Pair factors of 1995 are the pairs of numbers that when multiplied give the product 1995. The factors of 1995 in pairs are:

  • 1 × 1995 = (1, 1995)
  • 3 × 665 = (3, 665)
  • 5 × 399 = (5, 399)
  • 7 × 285 = (7, 285)
  • 15 × 133 = (15, 133)
  • 19 × 105 = (19, 105)
  • 21 × 95 = (21, 95)
  • 35 × 57 = (35, 57)

Negative pair factors of 1995 are:

  • -1 × -1995 = (-1, -1995)
  • -3 × -665 = (-3, -665)
  • -5 × -399 = (-5, -399)
  • -7 × -285 = (-7, -285)
  • -15 × -133 = (-15, -133)
  • -19 × -105 = (-19, -105)
  • -21 × -95 = (-21, -95)
  • -35 × -57 = (-35, -57)

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

Factors of 1995 Solved Examples

  1. Example 1: How many factors are there for 1995?

    Solution:

    The factors of 1995 are too many, therefore if we can find the prime factorization of 1995, 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 1995 = 31 × 51 × 71 × 191
    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 Least Common Multiple (LCM) and Greatest Common Divisor (GCD) of 1995 and 1655.

    Solution:

    The factors of 1995 are 1, 3, 5, 7, 15, 19, 21, 35, 57, 95, 105, 133, 285, 399, 665, 1995 and factors of 1655 are 1, 5, 331, 1655.

    Therefore, the Least Common Multiple (LCM) of 1995 and 1655 is 660345 and Greatest Common Divisor (GCD) of 1995 and 1655 is 5.

  3. Example 3: Find if 3, 7, 15, 35, 95, 105, 133 and 1948 are factors of 1995.

    Solution:

    When we divide 1995 by 1948 it leaves a remainder. Therefore, the number 1948 is not a factor of 1995. All numbers except 1948 are factors of 1995.

  4. Example 4: Find the product of all the prime factors of 1995.

    Solution:

    Since, the prime factors of 1995 are 3, 5, 7, 19. Therefore, the product of prime factors = 3 × 5 × 7 × 19 = 1995.

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FAQs on Factors of 1995

What are the Factors of 1995?

The factors of 1995 are 1, 3, 5, 7, 15, 19, 21, 35, 57, 95, 105, 133, 285, 399, 665, 1995 and its negative factors are -1, -3, -5, -7, -15, -19, -21, -35, -57, -95, -105, -133, -285, -399, -665, -1995.

What is the Sum of all Factors of 1995?

Sum of all factors of 1995 = (31 + 1 - 1)/(3 - 1) × (51 + 1 - 1)/(5 - 1) × (71 + 1 - 1)/(7 - 1) × (191 + 1 - 1)/(19 - 1) = 3840

What are the Prime Factors of 1995?

The prime factors of 1995 are 3, 5, 7, 19.

What is the Greatest Common Factor of 1995 and 281?

The factors of 1995 are 1, 3, 5, 7, 15, 19, 21, 35, 57, 95, 105, 133, 285, 399, 665, 1995 and the factors of 281 are 1, 281. 1995 and 281 have only one common factor which is 1. This implies that 1995 and 281 are co-prime.

Hence, the Greatest Common Factor (GCF) of 1995 and 281 is 1.

How Many Factors of 1995 are also Factors of 1952?

Since, the factors of 1995 are 1, 3, 5, 7, 15, 19, 21, 35, 57, 95, 105, 133, 285, 399, 665, 1995 and factors of 1952 are 1, 2, 4, 8, 16, 32, 61, 122, 244, 488, 976, 1952. Hence, 1995 and 1952 have only one common factor which is 1. Therefore, 1995 and 1952 are co-prime.

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