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X-ray flare (XRF) is a common phenomenon in the X-ray afterglow of gamma-ray bursts (GRBs). Although it is commonly believed that XRFs may share a common origin with prompt emission, i.e., the “internal” origin, the origin of XRFs is still unknown. In this work, we compile a GRB sample containing 31 GRBs with a single XRF, a well-measured spectrum, and a redshift, and investigate the intrinsic properties and correlations between prompt emission and the XRFs of these events. We find that the distributions of main physical parameters of prompt emission and XRFs are basically log-normal. The median value of the rise time is shorter than the decay time for all flares, with a ratio of about 1:2, which is similar to the fast rise and exponential decay structure of prompt emission pulses. We also find that the prompt emission energy (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>E</mi><mi>iso</mi></msub></semantics></math></inline-formula>) and peak luminosity (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mi>iso</mi></msub></semantics></math></inline-formula>) have tight correlations with XRF energy (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>E</mi><mrow><mi mathvariant="normal">X</mi><mo>,</mo><mi>iso</mi></mrow></msub></semantics></math></inline-formula>) and peak luminosity (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mrow><mi mathvariant="normal">X</mi><mo>,</mo><mi mathvariant="normal">p</mi></mrow></msub></semantics></math></inline-formula>), <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>E</mi><mi>iso</mi></msub><mo>∝</mo><msubsup><mi>E</mi><mrow><mi mathvariant="normal">X</mi><mo>,</mo><mi>iso</mi></mrow><mrow><mn>0.74</mn></mrow></msubsup></mrow></semantics></math></inline-formula> (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>L</mi><mrow><mi mathvariant="normal">X</mi><mo>,</mo><mi mathvariant="normal">p</mi></mrow><mrow><mn>0.62</mn></mrow></msubsup></semantics></math></inline-formula>) and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>L</mi><mi>iso</mi></msub><mo>∝</mo><msubsup><mi>E</mi><mrow><mi mathvariant="normal">X</mi><mo>,</mo><mi>iso</mi></mrow><mrow><mn>0.85</mn></mrow></msubsup></mrow></semantics></math></inline-formula> (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>L</mi><mrow><mi mathvariant="normal">X</mi><mo>,</mo><mi mathvariant="normal">p</mi></mrow><mrow><mn>0.68</mn></mrow></msubsup></semantics></math></inline-formula>). However, the durations of prompt emissions are independent of the temporal properties of XRFs. Furthermore, we also analyze the three-parameter correlations between prompt emissions and XRFs, and find that there are tight correlations among the XRF peak time (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mrow><mi mathvariant="normal">p</mi><mo>,</mo><mi mathvariant="normal">z</mi></mrow></msub></semantics></math></inline-formula>), <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mrow><mi mathvariant="normal">X</mi><mo>,</mo><mi mathvariant="normal">p</mi></mrow></msub></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>E</mi><mi>iso</mi></msub></semantics></math></inline-formula>/<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mi>iso</mi></msub></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>L</mi><mrow><mi mathvariant="normal">X</mi><mo>,</mo><mi mathvariant="normal">p</mi></mrow></msub><mo>∝</mo><msubsup><mi>T</mi><mrow><mi mathvariant="normal">p</mi><mo>,</mo><mi mathvariant="normal">z</mi></mrow><mrow><mo>−</mo><mn>1.08</mn></mrow></msubsup><msubsup><mi>E</mi><mrow><mi>iso</mi></mrow><mrow><mn>0.84</mn></mrow></msubsup></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>L</mi><mrow><mi mathvariant="normal">X</mi><mo>,</mo><mi mathvariant="normal">p</mi></mrow></msub><mo>∝</mo><msubsup><mi>T</mi><mrow><mi mathvariant="normal">p</mi><mo>,</mo><mi mathvariant="normal">z</mi></mrow><mrow><mo>−</mo><mn>1.09</mn></mrow></msubsup><msubsup><mi>L</mi><mrow><mi>iso</mi></mrow><mrow><mn>0.71</mn></mrow></msubsup></mrow></semantics></math></inline-formula>. Interestingly, these results are very similar to the properties of an X-ray plateau in GRBs, which indicates that X-ray flares and plateaus may have the same physical origin, and strongly supports that the two emission components originate from the late-time activity of the central engine.