1007129640 has 256 divisors, whose sum is σ = 3587224320. Its totient is φ = 223395840.

The previous prime is 1007129621. The next prime is 1007129653. The reversal of 1007129640 is 469217001.

1007129640 = T₃₂₉ + T₃₃₀ + ... + T₁₈₂₄.

It is a happy number.

1007129640 is a nontrivial binomial coefficient, being equal to C(44881, 2).

It is a super-3 number, since 3×1007129640³ (a number of 28 digits) contains 333 as substring. Note that it is a super-d number also for d = 2.

It is a Harshad number since it is a multiple of its sum of digits (30).

It is a junction number, because it is equal to n+sod(n) for n = 1007129598 and 1007129607.

It is an unprimeable number.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 829674 + ... + 830886.

It is an arithmetic number, because the mean of its divisors is an integer number (14012595).

Almost surely, 2^1007129640 is an apocalyptic number.

1007129640 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

1007129640 is the 44880-th triangular number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 1007129640, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1793612160).

1007129640 is an abundant number, since it is smaller than the sum of its proper divisors (2580094680).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

1007129640 is a wasteful number, since it uses less digits than its factorization.

1007129640 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1292 (or 1288 counting only the distinct ones).

The product of its (nonzero) digits is 3024, while the sum is 30.

The square root of 1007129640 is about 31735.3058910734. The cubic root of 1007129640 is about 1002.3709209580.

The spelling of 1007129640 in words is "one billion, seven million, one hundred twenty-nine thousand, six hundred forty".