Correct option is D
Given:-
128 identical marbles
Solution:-
The prime factorization of 128 is:
The number of distinct ways to arrange the marbles in a rectangular grid corresponds to finding the different pairs of factors of 128.
divisors of 128 are:
1,2,4,8,16,32,64,128
1,2,4,8,16,32,64,128
Pair of each divisor with its complement to form a rectangle.
The pairs are:
( 1,128)
( 1,128)
(2,64)
(4,32)
(8,16)
Total 4 distinct arrangements:
1×128
2×64
4×32
8×16
1×128
2×64
4×32
8×16
The number of distinct ways to arrange 128 identical marbles in a complete rectangular grid is 4
Thus, the correct answer is (D) 4
