LetK 6 be a real cyclic sextic number fields, andK 2, K3 be its quadratic and cubic subfields. Leth(L) denote the ideal class number of fieldL. Seven congruences forh =h(K6)/ h(K2)h(K3) are obtained. In particular, when conductorf 6 ofK 6 is primep, then $$Ch^ - \equiv B\frac{{p - 1}}{6}B\frac{{5\left( {p - 1} \right)}}{6}\left( {mod p} \right)$$ whereC is an explicitly given constant, andB n is the Bernoulli number. These results for real cyclic sextic fields are an extension of results for quadratic and cyclic quartic fields obtained by Ankeny-Artin-Chowla. Kiselev. Carlitz. Lu Hongwen, Zhang Xianke from 1948 to 1988.