The sum of the smallest two factors of an integer n is 6 and the sum of the two largest factor is 1122. Find n.

Guest Oct 26, 2019

#1**+1 **

**It could be 1,496:**

**1,496 =1 | 2 | 4 | 8 | 11 | 17 | 22 | 34 | 44 | 68 | 88 | 136 | 187 | 374 | 748 | 1496 (16 divisors)**

**Ignoring 1, then: 2 + 4 = 6 and 748 +374 =1,122**

Guest Oct 26, 2019

#2**+1 **

That wouldn't work since 1 and 1496 are also both factors. We know that the greatest factor of an integer n would n itself, and the smallest is 1. That would mean that the two smallest factors are 1 and 5, and the two greatest factors are n and 1122-n. We now use factor pairs to get that 1*n = 5(1122-n), or n = 5610-5n. Solving for n, we get that n = **935**.

ThatOnePerson Oct 27, 2019

#3**+1 **

The sum of the smallest two factors of an integer n is 6 and the sum of the two largest factor is 1122. Find n.

1 is a factor of every integer so the two smallest factors must be 1 and 5 which means that n is not divisable by 2 or by 3

The sum of the 2 largest factors is 1122. So the number n must be smaller than 1122/2 = 561

So one is 561-x and the other is 561+x

Maybe one is a multiple of 5 So maybe x=6t or 4t

x can't be 6t because 561 is divisable by 3 so 561*6t is also divisable by 3 which is not allowed.

What about x=4t

that would give us 561+4t and 561-4t

I cannot see any obvious reason why this can't be true.

I will try t values one at a time and see if I can find one that works

t | 1 |

565 | |

557 |

That one was easy, t =1 is a contender.

Well 565 does not have 2 or 3 as a factor and neither does 557 so they could be right.

557+565 = 1122

factor(565) = 5*113

factor(557) = 1+557

557*565 = 314705

So the number could be** 314705**

At this point in tme I am not convinced that this is the only possible answer though.

Melody Oct 27, 2019