设这个数是X.
340≡50（mod X）
X | 340-50=290
290=1×290=2×145=5×58=10×29
X=290,2,145,5,58,10,29
①若X=290 70÷290=0·····70 ×
②若X=2 70÷2=······0 110÷2=······0 160÷2=······0 ×
③若X=145 70÷140=0······70 ×
④若X=5 70÷5=······0 110÷5=······0 160÷5=······0 ×
⑤若X=58 70÷58=······12 110÷58=······52 ×
⑥若X=10 70÷10=······0 110÷10=······0 160÷10=······0 ×
⑦若X=29 70÷29=······12 110÷29=······23 160÷29=······15
12+23+15=50 √
X=29