The Prime Factorization Of 15

Factors of 15

Factors of 15 are the list of integers that tin be evenly divided into 15. It has a total of iv factors of which 15 is the biggest factor and the positive factors of 15 are 1, three, 5, and 15. The sum of all factors of fifteen is 24 and its factors in Pairs are (1, 15) and (3, 5).

• Factors of xv: i, 3, 5 and fifteen
• Negative Factors of 15: -i, -iii, -5 and -fifteen
• Prime number Factors of xv: 3, 5
• Prime number Factorization of xv: 3 × 5 = 3 × 5
• Sum of Factors of 15: 24

1.	What Are the Factors of 15?
2.	How to Calculate the Factors of xv?
3.	Factors of 15 by Prime number Factorization
iv.	Factors of 15 in Pairs
5.	FAQs on Factors of 15

What Are the Factors of xv?

The factor of whatsoever number includes the pair of numbers that give the number equally the result when they are multiplied with each other. In this case, xv is a composite number because it tin be divided by 1, 3, 5, and itself. Hence, 1, 3, 5 are the factors of 15. Likewise, all numbers are their own factors besides apart from number ane. Thus, 15 is also a gene of itself.

Of import Notes
All the numbers have at least two factors. Among these two numbers, the beginning factor is ane and the other is the number itself.

How to Summate the Factors of fifteen?

To find all the factors of 15, we have to make all the possible pairs of numbers and multiply them to see if the consequence is 15 or not.

For example, 1 × 15 = 15 and 2 × seven.five = 15, simply since a factor cannot be a decimal number, ii cannot be a gene of 15.

Similarly, 3 × 5 = 15, and 15 × one =  15

That's how you know that no other number apart from 1,three, five, and 15 is a factor of 15.

Explore factors using illustrations and interactive examples

• Factors of 37: The factors of 37 are i and 37.
• Factors of 21: The factors of 21 are i, 3, 7, and 21.
• Factors of 12:  The factors of 12 are 1, two, 3, 6, and 12.
• Factors of xl: The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40.
• Factors of 25: The factors of 25 are 1, 5 and 25

Factors of 15 by Prime Factorization

The factors of fifteen are 1, 3, v, and fifteen.

Let the states empathise this past performing prime factorization.

Now that we have washed the prime number factorization of 15, we can multiply it and get the other factors. Can you endeavor and find out if all the factors are covered or not? And equally you might accept already guessed, for prime number numbers, there are no other factors.

Factors of xv in Pairs

The pair factors tin can be whatsoever two numbers that, when multiplied with each other, gives the number as the product. In this case, the pair factors of 15 are:

iii × 5 = 15, hence, (iii,5) is a pair factor.

ane × xv = 15 is also a pair factor.

The positive pair factors of 15 are (one,15) and (3,5).

The negative pair factors of 15 are (-i,-15) and (-3,-five).

Tips and Tricks

• Did yous know that 1 is the smallest factor of all numbers?
• The given number is the largest factor of itself. For example, 6 is the largest cistron of itself, xiv is the largest factor of itself, and so on.

Solved Examples

1. Case 1Courtney has 5 friends. She has fifteen chocolates. Tin yous explain how Courtney should divide the fifteen chocolates and then that all her friends become an equal number of chocolates?

   Solution

   From the question, we know that she has v friends and 15 chocolates. Here, Courtney must use the concept of factors and multiples to carve up the chocolates amongst her friends as.

   Nosotros know that 15 is a multiple of five. We become the product 15 when we multiply five with 3.

   Therefore, Courtney should distribute 3 chocolates each to her friends to split up the chocolates equally.

2. Instance two A big foursquare box can fit upward to xv equal-sized small wrist-spotter boxes within it. If 3 wrist-picket boxes tin can be kept in one row of the big box, how many rows volition be required to keep all 15 boxes together in the big box?

   Solution

   Total number of wrist-lookout man boxes to exist kept in the large box = 15

   Total number of wrist-scout boxes in ane row = 3

   Now, if we simply divide 15 by 3, we get the answer 5, i.e. we need 5 rows of 3 wristwatches each to continue all the xv wrist-watch boxes in the big box.

   Here, we also learned that iii and 5, are the factors of fifteen.

   Therefore, five rows are required.

3. Instance 3

   Ashley is familiar with the concept of prime numbers. Hence, it will be easier for her to understand the factors of fifteen through prime number factorization. Tin you help her with it?

   Solution

   Since Ashley is familiar with prime numbers, we will showtime list out all the prime numbers less than 15 and run across how they divide fifteen.

   Prime number numbers less than fifteen are 2, 3, 5, 7, xi, and 13.

   Now, try to divide 15 with the above prime numbers.

   15 ÷ 2 = 7.5, only nosotros know that a factor cannot be a decimal number.

   15 ÷ 3 = 5; we have 5 as the respond, thus, 5 is the factor of xv.

   xv ÷ v = 3, here, three is also the factor of xv.

   xv ÷ 7 = 2.xiv, is not a gene of 15 as it is a decimal.

   Similarly, all the other prime numbers greater than v will give yous the answer in a decimal number, which ways that 5 is the highest prime cistron of 15. Also, it is one of the simply factors of 15 along with 1, 3, and xv itself.

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FAQs on Factors of 15

What are the Factors of 15?

The factors of 15 are 1, 3, five, 15 and its negative factors are -i, -3, -5, -15.

What is the Sum of the Factors of xv?

All the Factors of 15 are 1, 3, 5, 15 and therefore the sum of all these factors is i + 3 + five + fifteen = 24

What Numbers are the Prime Factors of xv?

The prime number factors of fifteen are 3, v.

What is the Greatest Mutual Factor of 15 and 10?

The factors of 15 and 10 are 1, iii, 5, xv and 1, ii, 5, 10 respectively.

Mutual factors of 15 and 10 are [1, 5].

Hence, the GCF of 15 and 10 is five.

What are the Common Factors of 15 and 9?

Since, the factors of 15 are one, 3, 5, xv and the factors of 9 are one, three, ix.
Hence, [1, 3] are the common factors of xv and nine.

The Prime Factorization Of 15,

Source: https://www.cuemath.com/numbers/factors-of-15/

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