Factors of 3 | How to Find the Prime Factors of 3 by the Prime Factorization Method? (2024)

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Factors of 3 | How to Find the Prime Factors of 3 by the Prime Factorization Method? ›

Prime Factorization of 3

To find the greatest common factor (GCF) between numbers, take each number and write its prime factorization. Then, identify the factors common to each number and multiply those common factors together. Bam!

Here, the number 3 is a prime number, so we cannot be able to split further. Thus, 3 is written as 1 × 3. Therefore, the prime factorization of 3 is 1 × 3 or 3.

Only 3 and 1 are factors of 3. Both positive and negative factors are multiples of three. Both positive and negative integers are possible for the factors and pair factors of 3.

Prime factorization of any number means to represent that number as a product of prime numbers. A prime number is a number that has exactly two factors, 1 and the number itself. For example, the prime factorization of 18 = 2 × 3 × 3. Here 2 and 3 are the prime factors of 18.

When a composite number is written as a product of all of its prime factors, we have the prime factorization of the number. For example, we can write the number 72 as a product of prime factors: 72 = 2 3 ⋅ 3 2 . The expression 2 3 ⋅ 3 2 is said to be the prime factorization of 72.

One way of finding the least common multiple is to use prime factorization. Prime factorization is decomposing a number into a product of prime numbers. When you have done this for three numbers, pick out the primes with the highest multiplicity and make their product. That number is the LCM (least common multiple).

To find the greatest common factor of two or more natural numbers, there are 3 methods that can be used - listing out of the common factors, prime factorization, and division method. Each method requires division and multiplication to obtain the GCF. For example, the GCF of 14 and 35 is 7.

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.

How to do prime factorization fast? ›

The question to ask is “what two numbers multiplied together equal 3?” Every factor can be paired with another factor and multiplying the two will result in 3. In this case, we can see that 3 is a prime number. By definition, a prime number is a number that doesn't have any other factors other than itself and 1.

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, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293.

A prime number is a number whose only whole factors are 1 and itself. The only positive integral multiple of 3 which is a prime number is 1×3=3 itself.

The number 3 is divisible only by 1 and the number itself. For a number to be classified as a prime number, it should have exactly two factors. Since 3 has exactly two factors, i.e. 1 and 3, it is a prime number.

A sphenic number has Ω(n) = 3 and is square-free (so it is the product of 3 distinct primes). The first: 30, 42, 66, 70, 78, 102, 105, 110, 114, 130, 138, 154 (sequence A007304 in the OEIS).