| ||||
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Cardinal | one hundred thirty-eight | |||
Ordinal | 138th (one hundred thirty-eighth) | |||
Factorization | 2 × 3 × 23 | |||
Divisors | 1, 2, 3, 6, 23, 46, 69, 138 | |||
Greek numeral | ΡΛΗ´ | |||
Roman numeral | CXXXVIII | |||
Binary | 100010102 | |||
Ternary | 120103 | |||
Senary | 3506 | |||
Octal | 2128 | |||
Duodecimal | B612 | |||
Hexadecimal | 8A16 |
138 (one hundred [and] thirty-eight) is the natural number following 137 and preceding 139.
138 is a sphenic number, [1] and the smallest product of three primes such that in base 10, the third prime is a concatenation of the other two: . [a] It is also a one-step palindrome in decimal (138 + 831 = 969).
138 has eight total divisors that generate an arithmetic mean of 36, [2] which is the eighth triangular number. [3] While the sum of the digits of 138 is 12, the product of its digits is 24. [4]
138 is an Ulam number, [5] the thirty-first abundant number, [6] and a primitive ( square-free) congruent number. [7] It is the third 47- gonal number. [8]
As an interprime, 138 lies between the eleventh pair of twin primes ( 137, 139), [9] respectively the 33rd and 34th prime numbers. [10]
It is the sum of two consecutive primes ( 67 + 71), [11] and the sum of four consecutive primes ( 29 + 31 + 37 + 41). [12]
There are a total of 44 numbers that are relatively prime with 138 (and up to), [13] while 22 is its reduced totient. [14]
138 is the denominator of the twenty-second Bernoulli number (whose respective numerator, is 854513). [15] [16]
A magic sum of 138 is generated inside four magic circles that features the first thirty-three non-zero integers, with a 9 in the center (first constructed by Yang Hui). [b]
The simplest Catalan solid, the triakis tetrahedron, produces 138 stellations (depending on rules chosen), [c] 44 of which are fully symmetric and 94 of which are enantiomorphs. [17]
Using two radii to divide a circle according to the golden ratio yields sectors of approximately 138 degrees (the golden angle), and 222 degrees.
| ||||
---|---|---|---|---|
Cardinal | one hundred thirty-eight | |||
Ordinal | 138th (one hundred thirty-eighth) | |||
Factorization | 2 × 3 × 23 | |||
Divisors | 1, 2, 3, 6, 23, 46, 69, 138 | |||
Greek numeral | ΡΛΗ´ | |||
Roman numeral | CXXXVIII | |||
Binary | 100010102 | |||
Ternary | 120103 | |||
Senary | 3506 | |||
Octal | 2128 | |||
Duodecimal | B612 | |||
Hexadecimal | 8A16 |
138 (one hundred [and] thirty-eight) is the natural number following 137 and preceding 139.
138 is a sphenic number, [1] and the smallest product of three primes such that in base 10, the third prime is a concatenation of the other two: . [a] It is also a one-step palindrome in decimal (138 + 831 = 969).
138 has eight total divisors that generate an arithmetic mean of 36, [2] which is the eighth triangular number. [3] While the sum of the digits of 138 is 12, the product of its digits is 24. [4]
138 is an Ulam number, [5] the thirty-first abundant number, [6] and a primitive ( square-free) congruent number. [7] It is the third 47- gonal number. [8]
As an interprime, 138 lies between the eleventh pair of twin primes ( 137, 139), [9] respectively the 33rd and 34th prime numbers. [10]
It is the sum of two consecutive primes ( 67 + 71), [11] and the sum of four consecutive primes ( 29 + 31 + 37 + 41). [12]
There are a total of 44 numbers that are relatively prime with 138 (and up to), [13] while 22 is its reduced totient. [14]
138 is the denominator of the twenty-second Bernoulli number (whose respective numerator, is 854513). [15] [16]
A magic sum of 138 is generated inside four magic circles that features the first thirty-three non-zero integers, with a 9 in the center (first constructed by Yang Hui). [b]
The simplest Catalan solid, the triakis tetrahedron, produces 138 stellations (depending on rules chosen), [c] 44 of which are fully symmetric and 94 of which are enantiomorphs. [17]
Using two radii to divide a circle according to the golden ratio yields sectors of approximately 138 degrees (the golden angle), and 222 degrees.