The C Major scale is considered to be the easiest scale to learn on the piano as it uses only the white notes of the piano starting on C. This is normally the first scale I teach students (both children and adults) starting with 1 and 2 octave hands separately and only once this is mastered would I suggest trying them hands together. You can increase the scale to 3 and 4 octaves quite simply by putting the thumb under again in the right hand and 4th in the left hand and repeating the fingering pattern again. In the earlier ABRSM piano grades you will only be expected to play the scale 1 and 2 octaves hand together or contrary motion (starting with both thumbs on middle C) however in later grades you’ll be expected to play it up to 4 octaves hands together. ABRSM piano scale books can be easily obtained locally from music shops in Swindon as well as online. Note that finger 3 in both hands are used at the same time when playing hands together.

Here is the piano fingering for the C Major scale as taught in my lessons:

One octave R.H (up) 12312345 (down) 4321321

One octave L.H (up) 54321321 (down) 2312345

Two octaves R.H (up) 123123412312345 (down) 43213214321321

Two octaves L.H (up) 543213214321321 (down) 23123412312345

Watch video demonstration of the teacher playing the C major scale: