Factors of 10011,10014 and 10016
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Solution Factors are numbers that can divide without remainder. Factors of 10011 10011/1 = 10011 gives remainder 0 and so are divisible by 110011/3 = 3337 gives remainder 0 and so are divisible by 3 10011/47 = 213 gives remainder 0 and so are divisible by 47 10011/71 = 141 gives remainder 0 and so are divisible by 71 10011/141 = 71 gives remainder 0 and so are divisible by 141 10011/213 = 47 gives remainder 0 and so are divisible by 213 10011/3337 = 3 gives remainder 0 and so are divisible by 3337 10011/10011 = 1 gives remainder 0 and so are divisible by 10011 Factors of 10014 10014/1 = 10014 gives remainder 0 and so are divisible by 110014/2 = 5007 gives remainder 0 and so are divisible by 2 10014/3 = 3338 gives remainder 0 and so are divisible by 3 10014/6 = 1669 gives remainder 0 and so are divisible by 6 10014/1669 = 6 gives remainder 0 and so are divisible by 1669 10014/3338 = 3 gives remainder 0 and so are divisible by 3338 10014/5007 = 2 gives remainder 0 and so are divisible by 5007 10014/10014 = 1 gives remainder 0 and so are divisible by 10014 Factors of 10016 10016/1 = 10016 gives remainder 0 and so are divisible by 110016/2 = 5008 gives remainder 0 and so are divisible by 2 10016/4 = 2504 gives remainder 0 and so are divisible by 4 10016/8 = 1252 gives remainder 0 and so are divisible by 8 10016/16 = 626 gives remainder 0 and so are divisible by 16 10016/32 = 313 gives remainder 0 and so are divisible by 32 10016/313 = 32 gives remainder 0 and so are divisible by 313 10016/626 = 16 gives remainder 0 and so are divisible by 626 10016/1252 = 8 gives remainder 0 and so are divisible by 1252 10016/2504 = 4 gives remainder 0 and so are divisible by 2504 10016/5008 = 2 gives remainder 0 and so are divisible by 5008 10016/10016 = 1 gives remainder 0 and so are divisible by 10016 |
Converting to factors of 10011,10014,10016
We get factors of 10011,10014,10016 numbers by finding numbers that can be multiplied together to equal the target number being converted.
This means numbers that can divide 10011,10014,10016 without remainders. So first number to consider is 1 and 10011,10014,10016
Getting factors is done by diving the number with numbers lower to it in value to find the one that will not leave remainder. Numbers that divide without remainders are the factors.
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Other number conversions to consider
Factors are the numbers you multiply to get another number. For instance, the factors of 25 are 5 and 5, because 5×5 = 25. Some numbers have more than one factorization (more than one way of being factored). For instance, 12 can be factored as 1×12, 2×6, or 3×4. A number that can only be factored as 1 times itself is called "prime". The first few primes are 2, 3, 5, 7, 11, and 13. The number 1 is not regarded as a prime, and is usually not included in factorizations, because 1 goes into everything. (The number 1 is a bit boring in this context, so it gets ignored.
By the way, there are some divisibility rules that can help you find the numbers to divide by. There are many divisibility rules, but the simplest to use are these: If the number is even, then it's divisible by 2. If the number's digits sum to a number that's divisible by 3, then the number itself is divisible by 3. If the number ends with a 0 or a 5, then it's divisible by 5.
Of course, if the number is divisible twice by 2, then it's divisible by 4; if it's divisible by 2 and by 3, then it's divisible by 6; and if it's divisible twice by 3 (or if the sum of the digits is divisible by 9), then it's divisible by 9. But since you're finding the factorization, you don't really care about these non-prime divisibility rules. There is a rule for divisibility by 7, but it's complicated enough that it's probably easier to just do the division on your calculator and see if it comes out even.
If you run out of small numbers and you are not done factoring, then keep trying bigger and bigger whole numbers (9, 14, 17, 20, 23, etc) until you find number that can divide without remainder. For example, 13 is a factor of 52 because 13 divides exactly into 52 (52 ÷ 13 = 4 leaving no remainder). The complete list of factors of 52 is: 1, 2, 4, 13, 26, and 52 (all these divide exactly into 52). If your number doesn't divide in, then the only potential divisors are bigger numbers. Since the square of your number is bigger than the number.