Question & Answer
QUESTION

Prime factors of 140 are:
(a) \[2\times 2\times 7\]
(b) \[2\times 2\times 5\]
(c) \[2\times 2\times 5\times 7\]
(d) \[2\times 2\times 5\times 7\times 3\]

ANSWER Verified Verified
Hint: We will use the definition of prime number and prime factors to find the prime factors of 140. Prime numbers are numbers having only two factors 1 and itself whereas prime factors are factors which are prime.

Complete step-by-step answer:
Before proceeding with the question, we should understand the concept of prime number and prime factors.
Prime numbers are whole numbers greater than 1, that have only two factors – 1 and the number itself. Prime numbers are divisible only by the number 1 or itself. For example, 2, 3, 5, 7 and 11 are the first few prime numbers.
A factor that is a prime number. In other words: any of the prime numbers that can be multiplied to give the original number. Example: The prime factors of 15 are 3 and 5 (because 3×5=15, and 3 and 5 are prime numbers).
We know that 140 is a composite number and a composite number is a positive integer that has at least one divisor other than one and itself.
So let us first find the factor pairs of 140, so we get,
\[\begin{align}
  & 140=1\times 140 \\
 & 140=2\times 70 \\
 & 140=4\times 35 \\
 & 140=5\times 28 \\
 & 140=7\times 20 \\
 & 140=10\times 14 \\
\end{align}\]
So factors of the number 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70. Now among these factors the prime factors according to the definition are 2, 2, 5 and 7 because \[140=2\times 2\times 5\times 7\].
Hence the correct answer is option (c).

Note: An alternative method can be a prime factorization method. Prime factorization is finding which prime numbers multiply together to make the original number.

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