From the zygote cells differentiate by 2^n. Here n is the number of divisions needed to attain the total number of cells.
Here 2^n = 10^13 = 10000000000000
After 10 divisions = 2^n = 1024 (n = 10)
After 20 divisions = 2^20 = 1048576
After 30 divisions = 2^30 = 1073741824
After 40 divisions = 2^40 = 1099511627776
Almost after 43 divisions or 43.3 divisions = 10829260783553
Hence, about 43 divisions are needed to attain 10^13 cells.