Abstract: It is proved that the SU(m+n)⊃SU(m)×SU(n) isoscalar factors (ISF) are equal to the S(f₁+S(f₂) outer-product ISF of the permutation group. Since the latter only depend on the partition labels, the values of the SU(m+n)SU(m)×SU(n) ISF do not depend on m and n explicitely. Consequently for a f(=(f₁+f₂)-particle system, by evaluating the S(f)⊃S(f₁)×S(f₂) outer-product ISF we can obtain all (an infinite number) of the SU (m+n)⊃SU(m)×SU(n) ISF (or the f₂-particle coefficients of fractional parentage) for arbitrary m and n at a single stroke, in stead of one m and one n at a time. A simple method, the eigenfunction method, is given for evaluating the SU(m+n)⊃SU(m)×SU(n) single particle ISF, while the many-particle ISF can be calculated in terms of the outer-product reduction coefficients and the transformation coefficients from the Yamanouchi basis to the S(f₁+f₂)⊃S(f₁)×S(f₂) basis.