Cactus spines are modified.

1.) leaves
2.) stems
3.) branches

Cactus spines are modified 1) LEAVES.

Cactus spines occur in clusters in the axil of leaves. Cactus spines are also known as modified bud scales, which also are modified leaves. The spine primordia is produced at the base of the axillary bud's shoot apical meristem; the location where leaf primordia also grows.

Though cactus spines are modified leaves, they do not contain any of the cells or tissues characteristics of leaves when they mature. Cactus spines consist of just a core of fibers surrounded by sclereid-like epidermis cells. When the spines mature, all the cells in the spines are dead. The only living cells are found at the base of the cactus which enables the spine to continue growing.