238 and Level 1
- 238 is a composite number.
- Prime factorization: 238 = 2 x 7 x 17.
- The exponents in the prime factorization are 1, 1 and 1.
- Factors of 238: 1, 2, 7, 14, 17, 34, 119, 238.
- Factor pairs: 238 = 1 x 238, 2 x 119, 7 x 34, or 14 x 17.
- Since 238 has no square number factors, its square root cannot be simplified.
234 and Level 3
- 234 is a composite number.
- Prime factorization: 234 = 2 x 3 x 3 x 13, which can be written 2 x (3^2) x 13.
- The exponents in the prime factorization are 1, 2 and 1.
- Factors of 234: 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234.
- Factor pairs: 234 = 1 x 234, 2 x 117, 3 x 78, 6 x 39, 9 x 26, or 13 x 18.
512 Ants and Level 4
- 512 is a composite number.
- Prime factorization: 512 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2, which can be written 512 = (2^9)
- The exponent in the prime factorization is 9.
- Factors of 512: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512.
- Factor pairs: 512 = 1 x 512, 2 x 256, 4 x 128, 8 x 64, or 16 x 32.
A Forest of 240 Factor Trees
- 240 is a composite number.
- Prime factorization: 240 = 2 x 2 x 2 x 2 x 3 x 5, which can be written 24 x 3 x 5.
- The exponents in the prime factorization are 4, 1 and 1.
- Factors of 240: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240.
For 201 to be a prime number, it would have been required that 201 has only two divisors, i.e., itself and 1. However, 201 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 201 = 3 x 67, where 3 and 67 are both prime numbers.
However, 12 is not a prime number, because 1 * 12 = 12, 2 * 6 = 12, and 3 * 4 = 12. Prime factorization means finding all the prime numbers that are factors of a number. 2 If the last digit is even, the number is divisible by 2.
The factors of 118. Answer : 1,2,59,118, Related Links : Is 118 a rational number?
When a number has more than two factors it is called a composite number. Here are the first few prime numbers: 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, etc.
For 263, the answer is: yes, 263 is a prime number because it has only two distinct divisors: 1 and itself (263). As a consequence, 263 is only a multiple of 1 and 263.
A prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole number that can be divided evenly into another number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29. Numbers that have more than two factors are called composite numbers.
For 115 to be a prime number, it would have been required that 115 has only two divisors, i.e., itself and 1. However, 115 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 115 = 5 x 23, where 5 and 23 are both prime numbers.
For 382, the answer is: No, 382 is not a prime number. The list of all positive divisors (i.e., the list of all integers that divide 382) is as follows: 1, 2, 191, 382. For 382 to be a prime number, it would have been required that 382 has only two divisors, i.e., itself and 1.
384 and Level 6
- 384 is a composite number.
- Prime factorization: 384 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3, which can be written 384 = (2^7) x 3.
- The exponents in the prime factorization are 7 and 1.
- Factors of 384: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384.
191 and Level 6
- 191 is a prime number.
- Prime factorization: 191 is prime.
- The exponent of prime number 191 is 1. Adding 1 to that exponent we get (1 + 1) = 2.
- Factors of 191: 1, 191.
- Factor pairs: 191 = 1 x 191.
- 191 has no square factors that allow its square root to be simplified. √191 ≈ 13.82027.
Answer and Explanation:
The prime factorization of 100 is 2 * 2 * 5 * 5. Using exponents, this number can also be written as 2^2 * 5^2.The factors of 72. Answer : 1,2,3,4,6,8,9,12,18,24,36,72, Related Links : Is 72 a rational number?
27 is a composite number. 27 = 1 x 27, or 3 x 9. Factors of 27: 1, 3, 9, 27. Prime factorization: 27 = 3 x 3 x 3, which can also be written 27 = 3³.
39 is a composite number. 39 = 1 x 39 or 3 x 13. Factors of 39: 1, 3, 13, 39. Prime factorization: 39 = 3 x 13.
In the prime factorization of 36 = 2² x 3², the two is used as a factor two times and the three is used as a factor twice. When checking to see if a number is prime or not, you need only divide by those prime numbers that when squared remain less than the given number.
Prime Factor. 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).
24 Think You Have a Snow Problem?Try This:
- 24 is a composite number.
- Prime factorization: 24 = 2 x 2 x 2 x 3, which can be written 24 = 2³ x 3.
- The exponents in the prime factorization are 3 and 1.
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.
- Factor pairs: 24 = 1 x 24, 2 x 12, 3 x 8, or 4 x 6.
99 is a composite number. 99 = 1 x 99, 3 x 33, or 9 x 11. Factors of 99: 1, 3, 9, 11, 33, 99. Prime factorization: 99 = 3 x 3 x 11, which can also be written 99 = 3² x 11.
Here is the basic factoring information for the number 100.
- 100 is a composite number.
- Prime factorization: 100 = 2 × 2 × 5 × 5, which can be written 100 = 2²× 5²
- The exponents in the prime factorization are 2 and 2.
- Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100.
