Question

state the fundamental theorem of arithmetic and thus show that (2×3×5×7×11+11) is a composite number.​

Answer 1

Answer:

it states, "Every composite number can be factorized as a product of primes,

Step-by-step explanation:

(2*3*5*7*11+11)

11(2*3*5*7*1+1)                                           ( took 11 common)

11(211)

since (2*3*5*7*11+11) has factors

it is a composite number

Answer 2

QuestioN :

state the fundamental theorem of arithmetic and thus show that ( 2 × 3 × 5  ×  7 × 11 + 11 ) is a composite number.​

GiveN :

• ( 2 × 3 × 5  ×  7 × 11 + 11 ) is a composite number.​

To FiNd :

• Fundamental theorem

ANswer :

211 is a prime number and cannot be broken

SolutioN :

Fundamental theorem as defined as that any number except 1 is either prime number or can be broken in prime number.

$\sf 2 \times 3 \times 5 \times 7 \times 11 + 11$

Taking 11 as common

$\sf 11(2\times3\times5\times7+1)$

$\sf 11(6\times25+1)$

$\sf 11(210+1)$

$\sf 11(211)$

211 cannot be factorized further.

∴ the given expression has 11 and 211 as its factor.

∴ Hence, the given number is composite.

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