Factors of 12? How to Find the Factors of 12 by Prime Factorization Method? (2024)

FAQs

Factors of 12? How to Find the Factors of 12 by Prime Factorization Method? ›

To find the prime factors, first we will divide the number 12 by its smallest prime factor, that is, 2. Now, divide by the next prime number, that is, 3. So, the prime factorization of 12 = 2 × 2 × 3 or \( 2^2\) × 3. This means that 2 and 3 are the prime numbers of 12.

For the number 12, we first factor 12 completely. We can't factor 12 any further, so 12 factored completely is 2 × 2 × 3. Both 2 and 3 are prime numbers, so we get that the prime factors of 12 are 2 and 3.

This means that 60, 72, and 84 should be the smallest three numbers with 12 factors. Let's check! 60 has the factors (1,2,3,4,5,6,10,12,15,20,30,60), 12 of them! 84 has the factors (1,2,3,4,6,7,12,14,21,28,42,84) again, 12!

Prime Factors of 12

To find the prime factors, first we will divide the number 12 by its smallest prime factor, that is, 2. Now, divide by the next prime number, that is, 3. So, the prime factorization of 12 = 2 × 2 × 3 or \( 2^2\) × 3. This means that 2 and 3 are the prime numbers of 12.

The simplest algorithm to find the prime factors of a number is to keep on dividing the original number by prime factors until we get the remainder equal to 1. For example, prime factorizing the number 30 we get, 30/2 = 15, 15/3 = 5, 5/5 = 1. Since we received the remainder, it cannot be further factorized.

∴ 12 = 2×2×3.

When expressed as a product of prime factors, 12 is written as 2² × 3. This is because 12 can be divided into 2 × 2 × 3, where 2 appears twice (hence 2²) and 3 appears once.

Factor Tree Method to Find Prime Factors of 12

Here, we can take it as 2 and pair it up with 6, as 2 multiplied by 6 gives 12. Step 2: 2 is a prime number, so it will remain unchanged and we can further split 6 into smaller prime factors. 6 can be further expressed as 2 multiplied by 3.

The factors of 12 are 1, 2, 3, 4, 6 and 12.

The prime numbers from 1 to 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

What is the formula for calculating factors? ›

For a number N, whose prime factorization is X^a × Y^b, we get the total number of factors by adding 1 to each exponent and then multiplying these together. This expresses the number of factors formula as, (a + 1) × (b + 1), where a, and b are the exponents obtained after the prime factorization of the given number.

Prime factorization is the breaking down of a number into the prime numbers that multiply to the original number. For example, the prime factorization of 12 is 2 * 2 * 3. We can add exponents when we have the same prime number occurring more than once. So, the prime factorization of 12 can also be written as 22 * 3.