Yes, the C_E_G or 1_3_5 of C all have the same scale degree or number system: 1_2_3_4_5_6_7_8
C: C_D_E_F_G_A_B_C
E: E_F#_G#_A_B_C#_D#_E
G: G_A_B_C_D_E_F#_G
All have: 1_2_3_4_5_6_7_8 as the scale degrees, the actual chords to the scale degres are as follows:
major
minor
minor
major
major
minor
1/2 dim.
major