Question

Express \[429\] as a product of its prime factors.

Answer 1

Hint:We are asked here to find the prime factors of the number \[429\]. Before proceeding you need to know what prime numbers are. Then check whether the number \[429\] is divisible by the first prime number, if not then try with the second prime number and when it’s completely divisible then break the quotient obtained into a product of prime numbers.

Complete step by step solution:
Given, the number \[429\] To express the number as the product of its prime factors, we need to first know what prime numbers are.

Prime numbers are numbers divisible by one and itself. The prime numbers are \[2,3,5,7.....\].

We now find the prime factors for the given number.

We will check with the first prime number that is \[2\] whether it divides \[429\] completely. Dividing
\[429\] by \[2\] we get \[1\] as remainder. That is, \[429 = 2 \times 214 + 1\]

Similarly, we check for the second prime number that is \[3\]. Dividing \[429\] by \[3\] we get that \[3\]
divides \[429\] completely, that is \[429 \div 3 = 143\]

We mean \[3\] is one of the prime factors of \[429\].
\[429\] can be written as,
\[429 = 3 \times 143\] (i)

Now, we can break \[143\] as \[11 \times 13\] and both are prime numbers, substituting this in equation (i) we get,
\[429 = 3 \times 11 \times 13\]

Therefore, the numbers \[3,\,11,13\] are all prime numbers that is \[3,\,11,13\] are the prime factors of the number \[429\].

Hence, \[429\] as a product of its prime factors can be written as,
\[429 = 3 \times \,11 \times 13\]

Note:There are two important classes of numbers. One is prime and composite numbers and another one is odd and even numbers. Prime numbers are divisible only by one and itself while composite numbers are divisible by at least one more number other than one and itself. Odd numbers are numbers which are not divisible by two while even numbers are numbers which are divisible by two.