Factors of 315 in pair are (1, 315) , (3, 105) , (5, 63) , (7, 45) , (9, 35) and (15, 21)

How to find factors of a number in pair

Steps to find factors of 315 in pair

Example: Find factors of 315 in pair

Factor Pair Pair Factorization
1 and 315 1 x 315 = 315
3 and 105 3 x 105 = 315
5 and 63 5 x 63 = 315
7 and 45 7 x 45 = 315
9 and 35 9 x 35 = 315
15 and 21 15 x 21 = 315

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 315. They are called negative pair factors.

Hence, the negative pairs of 315 would be ( -1 , -315 ) .

Definition of factor pairs?

In mathematics, factor pair are often given as pair of numbers which when multiplied together give the original number. Every natural number is a product of atleast one factor pair. Eg- Factors of 315 are 1 , 3 , 5 , 7 , 9 , 15 , 21 , 35 , 45 , 63 , 105 , 315. So, factors of 315 in pair are (1,315), (3,105), (5,63), (7,45), (9,35), (15,21).

What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

Properties of Factors

  • Every number is a factor of zero (0), since 315 x 0 = 0.
  • Every number other than 1 has at least two factors, namely the number itself and 1.
  • Every factor of a number is an exact divisor of that number, example 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315 are exact divisors of 315.
  • Factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315. Each factor divides 315 without leaving a remainder.

Steps to find Factors of 315

  • Step 1. Find all the numbers that would divide 315 without leaving any remainder. Starting with the number 1 upto 157 (half of 315). The number 1 and the number itself are always factors of the given number.
    315 ÷ 1 : Remainder = 0
    315 ÷ 3 : Remainder = 0
    315 ÷ 5 : Remainder = 0
    315 ÷ 7 : Remainder = 0
    315 ÷ 9 : Remainder = 0
    315 ÷ 15 : Remainder = 0
    315 ÷ 21 : Remainder = 0
    315 ÷ 35 : Remainder = 0
    315 ÷ 45 : Remainder = 0
    315 ÷ 63 : Remainder = 0
    315 ÷ 105 : Remainder = 0
    315 ÷ 315 : Remainder = 0

Hence, Factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, and 315

Frequently Asked Questions

  • Is 315 a composite number?

    Yes 315 is a composite number.

  • Is 315 a perfect square?

    No 315 is not a perfect square.

  • Write all odd factors of 315?

    The factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315.
    Odd factors of 315 are 1 , 3 , 5 , 7 , 9 , 15 , 21 , 35 , 45 , 63 , 105 , 315.

  • What is the mean of all prime factors of 315?

    Factors of 315 are 1 , 3 , 5 , 7 , 9 , 15 , 21 , 35 , 45 , 63 , 105 , 315. Prime factors of 315 are 3 , 3 , 5 , 7. Therefore mean of prime factors of 315 is (3 + 3 + 5 + 7) / 4 = 4.50.

  • What do you mean by proper divisors?

    A number x is said to be the proper divisor of y if it divides y completely, given that x is smaller than y.

Examples of Factors

Can you help Rubel in arranging 315 blocks in order to form a rectangle in all possible ways? For arranging 315 blocks in order to form a rectangle in all possible ways we need to find factors of 315 in pair.

Factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315. So, factors of 315 in pair are (1,315), (3,105), (5,63), (7,45), (9,35), (15,21).

Ariel has been asked to write all factor pairs of 315 but she is finding it difficult. Can you help her find out?

Factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315. So, factors of 315 in pair are (1,315), (3,105), (5,63), (7,45), (9,35), (15,21).

How many total number of factors of 315 in pair are possible?

Factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315. Hence, the factors of 315 in pair are (1,315), (3,105), (5,63), (7,45), (9,35), (15,21). Therefore, in total 6 pairs of factors are possible.

Sammy wants to write all the negative factors of 315 in pair, but don't know how to start. Help Sammy in writing all the factor pairs.

Negative factors of 315 are -1, -3, -5, -7, -9, -15, -21, -35, -45, -63, -105, -315. Hence, factors of 315 in pair are (-1,-315), (-3,-105), (-5,-63), (-7,-45), (-9,-35), (-15,-21).

Help Deep in writing the positive factors of 315 in pair and negative factor of 315 in pair.

Factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315. Positive factors of 315 in pair are (1,315), (3,105), (5,63), (7,45), (9,35), (15,21). Negative factors of 315 in pair are (-1,-315), (-3,-105), (-5,-63), (-7,-45), (-9,-35), (-15,-21).

Find the product of all factors of 315.

Factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315. So the product of all factors of 315 would be 1 x 3 x 5 x 7 x 9 x 15 x 21 x 35 x 45 x 63 x 105 x 315 = 976929722015625.

Find the product of all prime factors of 315.

Factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315. Prime factors are 3, 3, 5, 7. So, the product of all prime factors of 315 would be 3 x 3 x 5 x 7 = 315.

A student has been assigned the following tasks by the teacher:
- Finding out all positive factors of 315.
- Writing all prime factors of 315.
- Writing all the possible factors of 315 in pair.
Help him in writing all these.

Positive factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315.
Prime factors of 315 are 3, 3, 5, 7.
Factors of 315 in pair are (1,315), (3,105), (5,63), (7,45), (9,35), (15,21).