396/HK16. problem / Math - Solved Math Problems

MR-396 / 7. problem

Enter the logical value (true or false) of the following statements.

A: If a number is divisible by 6 and 8, it can also be divisible by 48.
B: If every digit of a positive integer is divisible by 3, then the number can also be divisible by 3.
C: The largest common divisor of 48 and 120 is 12.

Source: Magyarország: Unified final exam for high schools - Mathematics - intermediate level - 03.05.2016. - 7..)

Algebra → Exponential equations and inequalities → Exponential equations

A: Ha egy szám osztható 6-tal és 8-cal, akkor osztható 48-cal is.

B o n t s u k p r í m t é n y e z ő k r e a 6 - o t é s a 8 - a t .

6 = 2 \cdot 3

8 = 2 \cdot 2 \cdot 2

A 6 é s 8 l e g k i s e b b k ö z ö s t ö b b s z ö r ö s e :

L K T (6, 8) = 2^{3} \cdot 3 = 8 \cdot 3 = 24

M i v e l a 24 a l e g k i s e b b k ö z ö s t ö b b s z ö r ö s, e z é r t t r m é s z e t e s e n o s z t h a t ó 6 - a l é s 8 - a l i s, v i s z o n t n e m o s z t h a t ó 48 - a l!

A z A á l l í t á s H A M I S

B: Ha egy pozitív egész szám minden számjegye osztható 3-mal, akkor a szám is osztható 3-mal.

E g y s z á m a k k o r o s z t h a t ó h á r o m m a l, h a a s z á m j e g y e i n e k ö s s z e g e o s z t h a t ó 3 - a l .

H a a s z á m j e g y e k o s z t h a t ó a k 3 - a l, a k k o r a z o k ö s s z e g e i s o s z t h a t ó 3 - a l .

A z B á l l í t á s I G A Z

C: A 48 és a 120 legnagyobb közös osztója a 12.

48 : 24 = 2 \land 120 : 24 = 5

24 > 12

A z C á l l í t á s H A M I S

A : H A M I S B : I G A Z C : H A M I S