Prove every composite 3 digit integer has a prime factor less than or equal to 31.?

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Prove every composite 3 digit integer has a prime factor less than or equal to 31.?

2006-09-11 05:17:54 · 3 answers · asked by jjodom1010 3 in Science & Mathematics ➔ Mathematics

3 answers

The smallest composite number with no prime factor less than or equal to 31 would be 37*37 = 1369. (Note that 37 is the smallest prime greater than 31).
Therefore, any composite number less than 1369 must have a prime factor <=31.

2006-09-11 05:32:25 · answer #1 · answered by Bramblyspam 7 · 1⤊ 0⤋

32 times 32 is 1024 so any prime factors above 31 would generate a composite number of at least 4 digits...

2006-09-11 05:24:12 · answer #2 · answered by Andy FF1,2,CrTr,4,5,6,7,8,9,10 5 · 2⤊ 0⤋

It is simple as 1000 < 32^2
so compsite number <1000 has a factor < 1000*(1/2) < 32
so <= 31
QED

2006-09-11 05:22:46 · answer #3 · answered by Mein Hoon Na 7 · 2⤊ 0⤋