Is the word divorciaram the same in Brazilian and European Portuguese?

No.

While the spelling and the literal meaning of the word are identical, the answer is No because there is a significant difference in typical usage (syntax). In Brazilian Portuguese, the reflexive pronoun "se" is typically placed before the verb (proclisis), resulting in "se divorciaram." In Continental Portuguese, the standard usage is to place the pronoun after the verb (enclisis), resulting in "divorciaram-se." Additionally, a Portuguese person will almost always use a definite article before possessive pronouns (e.g., "os meus pais" instead of "meus pais").

Brazilian Portuguese Examples

1. Meus pais se divorciaram no ano passado. (My parents divorced last year.)
2. Eles se divorciaram de um jeito bem amigável. (They divorced in a very friendly way.)
3. Acho que eles se divorciaram por causa de problemas bobos. (I think they divorced because of silly problems.)
4. Os vizinhos se divorciaram e cada um foi morar em um apartamento. (The neighbors divorced and each moved into an apartment.)
5. Eles se divorciaram, mas continuam sendo amigos. (They divorced, but they continue to be friends.)

Continental Portuguese Examples

1. Os meus pais divorciaram-se no ano passado. (My parents divorced last year.)
2. Eles divorciaram-se de forma bastante amigável. (They divorced in a quite friendly way.)
3. Creio que eles se divorciaram por causa de problemas bobos. (I believe they divorced because of silly problems.)
4. Os vizinhos divorciaram-se e cada um foi morar para um apartamento. (The neighbors divorced and each moved to an apartment.)
5. Eles divorciaram-se, mas continuam a ser amigos. (They divorced, but they continue to be friends.)