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We report on the low-frequency noise performance of niobium dc superconducting quantum interference devices (SQUIDs), which contain nanobridges fabricated by focused ion beam lithography as the active Josephson elements. The devices have feature sizes down to 70 nm. We have measured devices of different loop sizes in two readout configurations: nano-scale loop sizes in small signal mode using a series SQUID array as a low-temperature pre-amplifier, and larger micron-scale loop sizes in a conventional flux-locked loop. We investigate the different contributions to the low frequency noise and report on electrical measurements made in applied magnetic fields of up to 0.5 T (in-plane) and 0.1 T (perpendicular to the plane) at operating temperatures around 7 K. We compare the measurements with the existing theories of noise in a dc SQUID.