136 (number)
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136 is a natural number that follows 135 and precedes 137. It is a three-digit number in the decimal system. In mathematics and number theory, 136 is noted for several properties that emerge from its prime factorization.
136 is an even composite number, meaning it has divisors other than 1 and itself. It is a highly useful number often used in examples of division and triangular numbers in teaching.
Mathematical properties
136 factorizes as 2 × 2 × 2 × 17, which can be written as 2³ × 17. Its divisors are 1, 2, 4, 8, 17, 34, 68, and 136—eight divisors in total. The sum of all its divisors is 270. Since the number of divisors (8) divides 136 itself (136 ÷ 8 = 17), it belongs to the class of numbers known as refactorable or tau numbers.
Triangular number
136 is a triangular number: it is the sum of the integers from 1 to 16, calculated as 16 × 17 ÷ 2 = 136. Triangular numbers represent the number of dots that can be arranged in an equilateral triangle, and 136 is the sixteenth such number.
Notation and other bases
In Roman numerals, 136 is written as CXXXVI. In binary, it is 10001000, which expresses 136 = 128 + 8. Additionally, 136 is 8 multiplied by 17, a property that makes it easily divisible into equal groups.