What are the factors of 12?
Factors of 12: 1, 2, 3, 4, 6, 12Negative factors: -1, -2, -3, -4, -6, -12
Pairs of factors: 1×12, 2×6, 3×4
Prime factors: 2, 2, 3
Number of positive factors: 6
Number of Negative factors: 6
A total number of factors = 12
Definition of factors in math
Multiplying two whole numbers to get the original/product number and a whole number that divides exactly into another number that is called factoring.Factors of 12 in pairs
Factors of 12 are- 1×12 = 12, 2×6 = 12, 3×4 = 12, as you can see we have multiplied two whole numbers with a combination of factors which gives the original/product number (12) in the result. We can find the Factors of 12 by multiplying two whole numbers in a pair to get the result 12.
Multiply by (1) 1 × 12 = 12
Multiply by (2) 2 × 6 = 12
Multiply by (3) 3 × 4 = 12
Multiply by (3) 3 × 4 = 12
Factors pairs of 12 = (1×12) (2×6) (3×4)
Add all these to our factors list
Factors list: -
Prime Factorization Of 12
Step 1: - We divide the given number(12) by the smallest prime number that divides the number exactly. We can easily divide 12 by the smallest prime number 2.
12/2 = 6
Step 2: - Divide the quotient again by the smallest or the next smallest prime number. We will repeat this process repeatedly until the quotient becomes 1.
12 ÷ 2 = 6
6 ÷ 2 = 3
3 ÷ 3 = 1
Prime factors are: -
2, 2, 3
Multiply all prime factors: -
2 × 2 × 3 = 12
Multiples of 12: -
12 × 1 = 1212 × 2 = 24
12 × 3 = 36
12 × 4 = 48
12 × 5 = 60
12 × 6 = 72
12 × 7 = 84
12 × 8 = 96
12 × 9 = 108
12 × 10 = 120
How many factors of 12?
12 has 6 factors (1, 2, 3, 4, 6, 12) and 12 with negative factors (-1, -2, -3, -4, -6, -12)How many odd and even factors of 12?
12 has (2) odd factors (1, 3) and (4) even factors (2, 4, 6, 12)
How to find the number of odd factors?
Step 1: - At, first find the prime factorization of given number.
12 = 2 * 2 * 3
Step 2: - Express them into exponential form.
2 to the power of 2 * 3 to the power of 1
2 * 2 * 3 = 2^2 * 3^1
Step 3: - To find the number of odd factors, you always have to write the exponent (1) in the base of 2. And then add (+1) in all other exponents.
2^0 * 3^1+1
2^0 * 3^2
2 = 2
Answer. The total number of odd factors is 2.How to find the sum of odd factors?
The first two steps are the same, factorization of the given number and expressing them in to exponential form.
12 = 2 * 2 * 3
2 * 2 * 3 = 2^2 * 3^1
If you want to find the sum of odd factors, you always have to write (0) in the exponent of 2. And besides them start all bases of the exponent from (0) and move up to maximum power of base and solve them.
2^0 * 3^0+3^1
1 * 1+3 = 4
Odd factors of 12
1, 3
Sum of odd factors
1 + 3 = 4
How to find the number of even factors?
Step 1: - At, first find the prime factorization of given number.
12 = 2 * 2 * 3
Step 2: - Express them into exponential form.
2 *2 * 3 = 2^2 * 3^1
Step 3: - Write the exponent of 2 as it is and then add (+1) to all other exponents.
2^2 * 3^1+1
2^2 * 3^2
Step 4: - Leave the base and multiply all exponents.
2 * 2 = 4
Answer. The number of even factors is 4.How to find the sum of even factors?
The first two steps are the same, factorization of the given number and expressing them in to exponential form.
12 = 2 * 2 * 3
2 * 2 * 3 = 2^2 * 3^1
Increase the exponent of 2 from 1 and move up to the maximum power of base.. And then increase exponents of all other bases from (0) and move up to the maximum power of base.
2^1+2^2 * 3^0+3^1
2+4 * 1+3
6 * 4 = 24
Answer. The sum of even factors is 24.Even factors of 12
2, 4, 6, 12
Sum of even factors
2 + 4 + 6 + 12 = 24
How to find the total number of factors?
Step 1: - At, first find the prime factorization of given number.
12 = 2 * 2 * 3
Step 2: - Express them into exponential form.
2 * 2 * 3 = 2^2 * 3^1
Step 3: - Leave the base (2,3) and raise all exponent by (+1) one.
2+1 * 1+1
3 * 2 = 6
Answer: Total number of factor is 6.How to find the sum of total factors?
The first two steps are the same, factorization of the given number and expressing them in to exponential form.
12 = 2 * 2 * 3
2 * 2 * 3 = 2^2 * 3^1
2^0+2^1+2^2 * 3^0+3^1
1+2+4 * 1+3
7 * 4 = 28
Answer. The sum of total factors is 28.All factors of 12
1, 2, 3, 4, 6, 12,
Sum of all factors
1 + 2 + 3 + 4 + 6 + 12 = 28
Some more questions: -
Q. Is 12 a composite number?
Yes! 12 is a composite number.Q. Is 12 a prime number?
No! 12 is not a prime number.Q. Is 12 a perfect square?
No! 12 is not a square number.Q. Is 12 an even number?
Yes! 12 is an even number.Q. Is 12 an odd number?
No! 12 is not an odd number.Q. Is 12 a rational number?
Yes! 12 is a rational number.Q. Is 12 a irrational number?
No! 12 is not an irrational number.Last words: - I hope this step-by-step tutorial was useful to teach you about the Factors of 12. Do you want to learn something else? So always come back to our site.
Thank you.
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