48 = 2^4 * 3. we need to check for 2^4 ka highest power and not 2 itself.2^31 has 7 as the highest power (7*4 =28) if we add another 2^4 it becomes 2^32 which is not feasible.
Get the prime factors of 48: 2^4×3^1 find the highest powers of 2 and 3 in 32! highest power of 2 is 31 in 32! highest power of 3 is 14 in 32! now divide highest power of 2 i.e [31/4] = 7 and [14/1] = 14 therefore maximum power of 48 is min(7,15) = 7
48=(2^4) *3. No. of 2's in 32! =31.Now no. of 2^4 in 2^31 is [31/4]=7...we have to determine power of 48 in 32! so first break 48 into prime factors and take the largest factor here it's 2^4.(since 2^4>3)
48= 2^4 *3 highest power of 3 in 32!= 32/3+10/3+3/3 =10+3+1= 14 highest power of 2 in 32!= 32/2+16/2+8/2+4/2+2/2= 16+8+4+2+1=31 highest power of 2^4 in 32!= 7 as 7 is least among 7 and 14, thus 7 will be the highest power
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