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# Factoring and Multiples

Leland Grant

Lvl 10
2021-09-30 20:42:30
4.83
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Cards in this guide (21)
What is the prime factorization of 24

You keep dividing 24 by prime numbers. You would get 2^3*3. A prime number has only 2 factors which are 1 and itself. Composite numbers are everything else except 1 and 0. 1 and 0 are neither prime, nor composite.

What is the prime factorization of 54

The prime factorization of 54 is 54=3*3*3*2
2 x 3 x 3 x 3 = 54
54 = 2 x 3 x 3 x 3

What is the prime factorization of 64

The prime factorization of 64 is 2x2x2x2x2x2 or 2^6.

2 x 2 x 2 x 2 x 2 x 2 = 64

What is the prime factorization of 34

The prime factorization of 34 is 2 x 17
2 x 17 = 34
The prime factorization of 34 is: 2 x 17
2 x 17 = 34

What is the prime factorization of 27

The prime factorization of 27 is 3 X 3 X 3. In exponential form it is 3 cubed.

Here is a factor tree:

27

3 x 9

3 x 3 x 3
3 x 3 x 3

What is the prime factorization of 12

The prime factorization of 12 is 2 x 2 x 3

What is the prime factorization of 30

The prime factorization of 30 is 2 * 3 * 5

Start with the lowest prime number that will divide into the given number evenly.

The result will be one of the prime factors and a number that might need to be factored. In the case of 30, 2 is a prime number and 15 needs to be factored further.

The lowest number that will divide into 15 evenly is 3. 3 * 5 equals 15. 5 is also a prime number, so the prime factorization of 30 is 2 * 3 * 5.

To find the prime factors of any number then divide the number by prime numbers of increasing value. When a prime number wholly divides the original number repeat the process with the same prime number but each time with the new quotient until complete division does not occur. Repeat with a prime number of higher value until the final quotient is 1.

30 ÷ 2 = 15

15 ÷ 2 complete division does not occur

15 ÷ 3 = 5

5 ÷ 3 complete division does not occur

5 ÷ 5 = 1 : quotient = 1, prime factorization is complete

The prime factors are therefore 2, 3 and 5.
2 x 3 x 5 = 30

What is the prime factorization of 33

33 = 3 x 11.
3 x 11

What is the prime factorization of 42

The prime factorization of 42 is 2 x 3 x 7.
2 x 3 x 7 = 42
2 x 3 x 7 = 42

What is the prime factorization of 52

The prime factorization of 52 is 2 x 2 x 13
2 x 2 x 13 = 52
2 x 2 x 13 = 52

What is the Prime factorization of 40

The prime factorization of 40 is 2 X 2 X 2 X 5 or 2^3 x 5.

To find the prime factorization of 40, find the lowest prime factor that will divide into 40.

That number is 2, and 2 X 20 equals 40. 2 is prime, so it is one of the factors. 20 is a composite number, so must be factored.

The lowest prime number that will divide evenly into 20 is 2. 2 X 10 equals 20. Another 2 is in the prime factorization, so you have 2 X 2 X 10. Ten is not a prime number, so the factoring has to continue.

2 X 5 equals 10. both numbers are prime, so now all you have to do is write out the factorization.

What is the prime factorization of 44

The prime factorization of 44 is 2 X 2 X 11

The factors of 44 are: 1, 2, 4, 11, 22, 44.

Factors can be prime and composite. In prime factorization, all the factors must be prime numbers.
2 x 2 x 11 = 44
2 x 2 x 11 = 44

What is the prime factorization of 46

The prime factorization of 46 is: 2 x 23

What is the prime factorization of 62

62 = 2 * 31
The prime factorization of 62 is 2 x 31.

What is the prime factorization of 57

The prime factorization of 57 is 3 x 19 = 57
3*19

What is the prime factorization of 6

2 x 3 is the prime factorization of 6.

What is the prime factorization of 22

The prime factorization of 22 is: 2 x 11 = 2

What is the prime factorization of 51

The prime factorization of 51 = 3 * 17

What is the prime factorization of 48

48 = 2 × 2 × 2 × 2 × 3 = 2⁴ × 3

What is the prime factorization of 74

2 x 37

What is the prime factorization of 954

2 x 3 x 3 x 53

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