To find the highest power of 8 that divides 88, we start with the prime factorization of 88.
- The prime factorization of 88 is 23×112^3\times 1123×11 because 88=2×2×2×1188=2\times 2\times 2\times 1188=2×2×2×11
- Since 8=238=2^38=23, the highest power of 8 dividing 88 depends on how many times 2 appears in the factorization of 88.
- Here, 232^323 is present exactly once in 88, so the highest power of 8 dividing 88 is 81=88^1=881=8.
Thus, the highest power of 8 that divides 88 is 818^181 or simply 8.
