JDK-8270378 added Math.divideExact() for symmetry with multiplyExact() and to account for the special cases of the division operator '/' where Integer.MIN_VALUE / -1 == Integer.MIN_VALUE and Long.MIN_VALUE / -1 == Long.MIN_VALUE. The same special case also occurs for floorDiv(int,int) as stated in its specification:

"Returns the largest (closest to positive infinity) int value that is less than or equal to the algebraic quotient. There is one special case, if the dividend is the Integer.MIN_VALUE and the divisor is -1, then integer overflow occurs and the result is equal to the Integer.MIN_VALUE."

The analogous special case obtains as well for floorDiv(long,long). Instead of ignoring the numeric overflow, a method floorDivExact() would throw an ArithmeticException when the dividend is the respective MIN_VALUE and the divisor is -1.