The cubic and cylindrical compressive strength tests of concrete could lead to different results. However, in order to reach a unit definition, most of international codes defines the specific compressive strength of concrete as the compressive strength of a 150*300mm cylindrical specimen. In addition to shape of the specimen size of the specimen could affect the results of the tests. In this regard, there is different factors for different shapes and sizes of specimens. You can find these factors in ACI318 code.
The strength of cylinder with diameter of 15 cm and 30 cm height can be approximated as 0.84 of the strength of a 15x15x15 cm cube according to Eurocodes.This ratio can be variable for different type of concrete for example it can be reach to 1 for high strength concrete.
The conversion factor based on type of concrete (NSC, HSC, VHSC, and UHPC) with or without fibre. Please go through the attached article for more information.
An evaluation with a large range of concrete strength (fc = 10 - 100 MPa, 680 samples) shows that the conversion factor has a mean value of 0.84 and an associated variation coefficient of 0.095, see the following paper:
Article Uncertainties of concrete parameters in shear capacity calcu...
This confirms the answer of Zainab Hashim Abbas presented above.
Factor of Safety (FOS) of 1.5 is applied beacuse in practice or on Site the Concrete sections(Beam, Column,Slab) are not of 150mm size,they are much greater.
So hence when we consider the Characteristic strength of concrete while designing,we apply a FOS of 1.5 to the fck, so that comes out to be “0.67 fck”.
When you apply compressive stresses on the Cylindrical Specimen in CTM,due to its height i.e 300mm,the slender effect causes the cylinder to bear comparatively lesser amount of stress,when compared to a Cube(150mm) causing the cylinder to get crushed.
For high strength concrete the factor change from (0.8-0.85) for normal concrete to be (0.89-0.99). Also the heat treatment has to be taken into account. On other hand, some researcher (Yuliarti Kusumawardaningsih et al.) states in his article that the cylinders may give higher strength than the cubes, but he did not perform any process of heat treatment.