You are watching: What is the least positive integer that is not a factor of 25

chen chen

25！=1*2*3*4*5*6*...23*24*25

26= 2*1328=2*14or 4*736=2*18or 3*12 or 4*956=7*8All products above are inside 25! so they are all factors of 25!But 58=2*29 and 29 is not inside 25! for this reason it"s no a variable of 25!

Jun 27, 2019•Comment

Michelle Scire

So why doesn"t the 2 count together a element of 25? it is what ns am perplexed on.

Apr 9, 2018•Comment

Sam Kinsman

Hi Michelle!

Actually, 2 is a element of 25! store in mind that 25! = 1*2*3*4*5.....*24*25. This perform of number is divisible by 2, so as such 2 is a variable of 25!

When we find that 29 is the smallest prime number that is snucongo.orgater than 25, us multiply 29 by 2 (because the answer cannot be a element number, therefore 29 chin doesn"t work). We acquire 58. You"re appropriate that 58 is divisible by 2, and that 2 is a element of 25 - but that doesn"t matter here, because even though 2 is a aspect of 25, the number 58 is not a variable of 25!. In various other words, 25! is no divisible by 58. Therefore that"s why 58 is the number we"re looking for :)

Apr 11, 2018•Reply

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I wonder the passage.I thought passage to speak "not a aspect of 25! and also not a element number". So I believed 26 is likewise correct. Due to the fact that 26 is no a variable (yes 2*13 is element of 25! but 26 is much more than 25!. So i thought just 26, no 2 and also 13) and also it"s not prime number.

If the answer was 58 prefer explanation indigenous other, passage need to say favor this,"the least positive essence that"s element is no a element of 25!"

I thought It"s about English Expression, am ns wrong? what component of passage say number"s factor is not a element of 25! not just hall number?

Mar 2, 2018•Comment

David Recine

This isn"t a issue of the English wording exactly. Instead, what you should understand right here is that also if a number is snucongo.orgater than 25 (without the exclamation point), it might still be a element of 25! (25 with the exclamation allude at the end, or 25 factorial).

Bear in mind the 25! is in reality a very huge number. The is the product the 25, multiplied by every positive totality number the is less than 25. The ultimate product is a number that is end 25 digits long. As a result, countless very huge numbers, consisting of 26 and numbers in the hundreds, thousands, millions, billions, etc... Can be determinants of 25!

For a number to not be a factor of 25!, it have to be larger than 25! AND also not it is in a product the the numbers that room multiplied by each various other to obtain the product of 25!

Since 25! is 25 multiplied by every entirety positive number much less than 25, it includes 13 multiplied by 2, which equals 26. In various other words, if 25! deserve to be separated evenly by 13*2, then it deserve to be divided by 26.

For this reason, 27 (9*3), 28 (7*4), 36 (9*4), and also 56 (14*4) also are components of 25! A number being larger than 25 does not immediately make it not a factor of 25!. Instead, a number larger than 25 is just *possibly* not a aspect of 25! friend still need to check any type of 25+ number to view if its element factorization consists entirely of factors that have the right to be uncovered within 25!