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125 is a composite number. 125 = 1 x 125 or 5 x 25. Factors of 125: 1, 5, 25, 125. Prime factorization: 125 = 5 x 5 x 5, which can also be written 125 = 5³. 125 is never a clue in the FIND THE FACTORS puzzles. Placing the last few factors on this Level 4 puzzle may be a bit trickier than usual. As always, use logic, not guessing and checking, to find its one and only solution. Good luck! Excel file of this week’s puzzles and last week’s factors: 12 Factors 2014-05-19 To find the prime factorization, divide #125# by only prime numbers. Remember that prime numbers are whole numbers greater than #1# that are only evenly divisible by themselves and #1#. Since #125# ends in #5#, it is evenly divisible by #5#, which is a prime number. (How convenient!) #125 -: 5 = 25# #25# now has to be factored into its prime factors. #25 = 5 * 5# So, the prime factorization of #125# is #125 = 5*5*5 = 5 ^3#
Prime Factorization Calculator
Here is the answer to questions like: Find the prime factorization of 125 using exponents or is 125 a prime or a composite number? Use the Prime Factorization tool above to discover if any given number is prime or composite and in this case calculate the its prime factors. See also in this web page a Prime Factorization Chart with all primes from 1 to 1000.
The prime factorization is the decomposition of a composite number into a product of prime factors that, if multiplied, recreate the original number. Factors by definition are the numbers that multiply to create another number. A prime number is an integer greater than one which is divided only by one and by itself. For example, the only divisors of 7 are 1 and 7, so 7 is a prime number, while the number 72 has divisors deived from 23•32 like 2, 3, 4, 6, 8, 12, 24 ... and 72 itself, making 72 not a prime number. Note the the only "prime" factors of 72 are 2 and 3 which are prime numbers. Prime factorization example 1Let's find the prime factorization of 72. Solution 1Start with the smallest prime number that divides into 72, in this case 2. We can write 72 as: 72 = 2 x 36 Now find the smallest prime number that divides into 36. Again we can use 2, and write the 36 as 2 x 18, to give. 72 = 2 x 2 x 18 18 also divides by 2 (18 = 2 x 9), so we have: 72 = 2 x 2 x 2 x 9 9 divides by 3 (9 = 3 x 3), so we have: 72 = 2 x 2 x 2 x 3 x 3 2, 2, 2, 3 and 3 are all prime numbers, so we have our answer. In short, we would write the solution as: 72 = 2 x 36 72 = 2 x 2 x 18 72 = 2 x 2 x 2 x 9 72 = 2 x 2 x 2 x 3 x 3 72 = 23 x 32 (prime factorization exponential form) Solution 2Using a factor tree:
See how to factor the number 72:
Taking the left-hand numbers and the right-most number of the last row (dividers) an multiplying then, we have 72 = 2 x 2 x 2 x 3 x 3 72 = 23 x 32 (prime factorization exponential form) Note that these dividers are the prime factors. They are also called the leaves of the factor tree. Prime factorization example 2See how to factor the number 588:
Taking the left-hand numbers and the right-most number of the last row (dividers) an multiplying then, we have 588 = 2 x 2 x 3 x 7 x 7 Prime Factorization Chart 1-1000
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