Q&A for How to Factor a Number

When multiplying numbers with decimals, follow the same multiplication process as you would with whole numbers, ensuring to account for the decimals after the calculation. The number of decimal places in your product should correspond to the total sum of decimal places in your factors.

Any number ending in 0 or 5 would have 5 as a factor (e.g. 35, 450, or 764,545,230).

It is customary but not mandatory, unless the instructions tell you to do so.

No. Factoring only has to do with multiplication and division, since you are determining the factors of a number.

Any prime number (such as 7) is factored only into itself and 1.

The greatest common factor (GCF) of some numbers is the largest number that divides evenly into all of the numbers. For example, the GCF of 10,15, and 25 is 5. See How to Find the Greatest Common Factor if you need more help.

2 is a prime number, so its factors are 1 and itself.

Yes, you can do it with any number of digits.

Yes. Whenever you look for the prime factors of any number you essentially form a prime-factor tree.

79 is a prime number. That means it cannot be evenly divided by any whole numbers other than itself and 1. So its only factors are 1 and 79.

Because the factors of 4 are 1, 2,and 4, while a prime number has only two factors -- 1 and itself.

Technically any number -- prime or not -- can be a factor. However, the factoring process is not really finished until you have reduced all factors to prime numbers. So yes, you want to keep factoring until you arrive at nothing but prime numbers. For example, 30 can be factored into 3 and 10; but 10 can be factored to 2 and 5. Thus, fully factoring 30 results in 2, 3, and 5, all prime numbers.

Both numbers are divisible by 17. 323 = 17 x 19. 391 = 17 x 23.

All numbers have factors. 144 is the square of 12, meaning that it equals 2 x 2 x 3 x 2 x 2 x 3 = 2^4 x 3².

A prime number is a number divisible only by 1 and itself.

It's 112.

A "prime number" is one whose factors are that number and 1. There are many combinations, but we don't consider 1 as prime.

The factors of 34 are 1, 2, 17 and 34.

If you mean (8n + 40), that is (2³)(n + 5). If you mean those two numbers separately, the factors of 8n are 2³ and n. The factors of 40 are 2³ and 5.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96.

If you have broken the number down into nothing but prime numbers, you have listed all of the factors.

If you mean 2x² - 5x - 3 = 0, the factors are (2x + 1) and (x - 3 ).

Either of the methods shown above will work well with 100. Divide by 2 twice, and then divide by 5.

Factorisation as described in the article doesn't apply to decimal numbers, it can only be done with whole numbers (numbers without a decimal). A possible interpretation of the factorisation of a decimal would be to write it its most reduced fractional form and then factorise the numerator and denominator. For example, 3.45 is equal to 345/100, which can be simplified to 69/20. The prime factorisation of 69 is 3*23 and for 20, it is 2*2*5, so 3.4 = (3*23)/(2*2*5). A consequence of this method is that numerator and denominator will never have prime factors in common; if they had, you could simplify the fraction by dividing numerator and denominator by that prime factor.

The last technique with two columns is for large numbers such as numbers in the thousands.

It depends on the type of root. A square root is the number multiplied by itself to get the result; for example, the square root of 64 is 8. (8 times 8 is 64). In cube root, the same number has to be multiplied thrice to give that number; for example, the cube root of 121 is 11. (11 times 11 times 11 equals 121.) If it's the square root you're looking for, you can use the methods in Calculate a Square Root by Hand .

The factors of 9 are 1, 3 and 9. The prime factorisation of 9 is 3*3, so the smallest prime factor is 3.