We present a novel approach for claim verification from tabular data documents. Recent LLM-based approaches either employ complex pretraining/fine-tuning or decompose verification into subtasks, often lacking comprehensive explanations and generalizability. To address these limitations, we propose a Multi-Agentic framework for Claim verification (MACE) consisting of three specialized agents: Planner, Executor, and Verifier. Instead of elaborate finetuning, each agent employs a zero-shot Chain-of-Thought setup to perform its tasks. MACE produces interpretable verification traces, with the Planner generating explicit reasoning strategies, the Executor providing detailed computation steps, and the Verifier validating the logic. Experiments demonstrate that MACE achieves state-of-the-art (SOTA) performance on two datasets and performs on par with the best models on two others, while achieving 80--100\% of best performance with substantially smaller models: 27--92B parameters versus 235B. This combination of competitive performance, memory efficiency, and transparent reasoning highlights our framework's effectiveness.