Prime factorization method for 31.36
Only whole numbers have a prime factorization.
In any case, just start checking primes, starting with 2,3,... to see which ones divide your number, and how many times.
To find the prime factorization of a number, we need to break it down into its prime factors, which are the prime numbers that multiply together to give the original number.
To find the prime factorization of 31.36, you can follow these steps:
Step 1: Determine if the number is even
Since 31.36 is a decimal number, it is not even. We'll need to convert it into a fraction before proceeding.
Step 2: Convert the decimal number into a fraction
To do this, we write the decimal as a fraction:
31.36 = 3136/100
Step 3: Simplify the fraction (if possible)
The fraction 3136/100 can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD is 4, so we divide 3136 by 4 and 100 by 4:
3136 ÷ 4 = 784
100 ÷ 4 = 25
The simplified fraction is 784/25.
Step 4: Factorize the numerator and denominator
To find the prime factorization of 784 and 25, we'll list their factors:
Factors of 784: 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784
Factors of 25: 1, 5, 25
Step 5: Identify the prime factors
From the factors listed above, we can see that the prime factors of 784 are 2, 2, 2, 2, and 7, since 2 × 2 × 2 × 2 × 7 = 784.
The prime factors of 25 are 5 and 5, since 5 × 5 = 25.
Step 6: Write the prime factorization
To express 31.36 as its prime factorization, we put all the prime factors together:
31.36 = (2 × 2 × 2 × 2 × 7)/(5 × 5) = (2^4 × 7)/(5^2)
Therefore, the prime factorization of 31.36 is (2^4 × 7)/(5^2).