Question

Samyak has an integer 2926 he wonders what is the minimum number x he needs such that on writing x as the sum of positive numbers the product of these positive numbers is equal to 2926​

Answer 1

Answer:

x is 1 my be right or not

Step-by-step explanation:

ok

Answer 2

✪ANSWER✪

• Minimum x = 39

★EXPLAINATION★

The prime factorization of 2926 is

$2926 = 2\times 7\times 11\times 19$

Following are possible value of x

$x = 1 + (2\times 7\times 11\times 19)$

$\:\:\:= 1 + 2926 = 2927$

$x = 2 + (7\times 11\times 19)$

$\:\:\:= 2+1463 = 1465$

$x=7 + (2\times 11\times 19)$

$\:\:\: =7+418 = 425$

$x = 11 + (2\times 7\times 19)$

$\:\:\:= 11+266= 277$

$x = 19 + (2\times 7\times 11)$

$\:\:\:=19+154= 173$

$x = (2\times 7)+(11\times 19)$

$\:\:\:=14+209= 223$

$x = (2\times 11)+(7\times 19)$

$\:\:\:=22+133= 155$

$x = (2\times 19)+(7\times 11)$

$\:\:\:=38+77= 115$

$x = 1+1 + (2\times 7\times 11\times 19)$

$\:\:\: = 1 +1+ 2926 = 2928$

$x = 1+2 + (7\times 11\times 19)$

$\:\:\:= 1+2+1463 = 1466$

$x=1+7 + (2\times 11\times 19)$

$\:\:\: =1+7+418 = 426$

$x = 1+11 + (2\times 7\times 19)$

$\:\:\:=1+ 11+266= 278$

$x = 1+19 + (2\times 7\times 11)$

$\:\:\:= 1+19+154= 174$

$x = 1+(2\times 7)+(11\times 19)$

$\:\:\:= 1+14+209= 224$

$x = 1+(2\times 11)+(7\times 19)$

$\:\:\:=1+22+133= 156$

$x = 1+(2\times 19)+(7\times 11)$

$\:\:\:= 1+38+77= 116$

$x = (2\times 7)+11+ 19$

$\:\:\:= 14 + 11+19 = 44$

$x = (2\times 11)+7+ 19$

$\:\:\:= 22 + 7 +19 = 48$

$x = (2\times 19)+7+ 11$

$\:\:\:= 38 + 7 +11 = 56$

$x = (7\times 11)+2+ 19$

$\:\:\:= 77 + 2+19 = 98$

$x = (7\times 19)+2+ 11$

$\:\:\:= 133 + 2 +11 =146$

$x = (11\times 19)+2+ 7$

$\:\:\:= 209 + 2 +7 = 218$

$x = 1+1+1 + (2\times 7\times 11\times 19)$

$\:\:\: = 1+1 +1+ 2926 = 2929$

$x = 1+1+2 + (7\times 11\times 19)$

$\:\:\:= 1+1+2+1463 = 1467$

$x=1+1+7 + (2\times 11\times 19)$

$\:\:\: =1+1+7+418 = 427$

$x = 1+1+11 + (2\times 7\times 19)$

$\:\:\:=1+1+ 11+266= 279$

$x = 1+1+19 + (2\times 7\times 11)$

$\:\:\:=1+ 1+19+154= 175$

$x = 1+1+(2\times 7)+(11\times 19)$

$\:\:\:=1+ 1+14+209= 225$

$x = 1+1+(2\times 11)+(7\times 19)$

$\:\:\:=1+1+22+133= 157$

$x = 1+1+(2\times 19)+(7\times 11)$

$\:\:\:= 1+1+38+77= 117$

$x = 1+(2\times 7)+11+ 19$

$\:\:\:= 1+14 + 11+19 = 45$

$x = 1+(2\times 11)+7+ 19$

$\:\:\:= 1+22 + 7 +19 = 49$

$x =1+ (2\times 19)+7+ 11$

$\:\:\:= 1+38 + 7 +11 = 57$

$x = 1+(7\times 11)+2+ 19$

$\:\:\:= 1+77 + 2+19 = 99$

$x = 1+(7\times 19)+2+ 11$

$\:\:\:= 1+133 + 2 +11 =147$

$x =1+ (11\times 19)+2+ 7$

$\:\:\:= 1+209 + 2 +7 = 219$

$x = 2+ 7 + 11 + 19 = 39$

It is clear from these that x = 39 is the least value of x which satisfy the condition given in question.