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Atlas › Integer Profiles › Node 10,076,670

10,076,670

2 × 33 × 5 × 37321
Abundant Even Composite

10,076,670 factors as 2 × 3^3 × 5 × 37321. Its 32 positive divisors give a proper-divisor sum of 16,795,170, so this integer is abundant. The Collatz stopping time is 114 steps.

Prime Factor Structure

Factorization String 2 × 3^3 × 5 × 37321
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 26,871,840
Proper Divisor Sum 16,795,170
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #10076653 ← → #10076681

Radix Representation

Decimal 10076670
Binary 100110011100000111111110 (24 bits)
Octal 0o46340776
Hexadecimal 0x99C1FE

Divisor Catalog (32)

1 2 3 5 6 9 10 15 18 27 30 45 54 90 135 270 37,321 74,642 111,963 186,605 223,926 335,889 373,210 559,815 671,778 1,007,667 1,119,630 1,679,445 2,015,334 3,358,890 5,038,335 10,076,670

Collatz Trajectory (114 steps to reach 1)

Iterative sequence n → n/2 (if even) or 3n+1 (if odd):

10,076,670 5,038,335 15,115,006 7,557,503 22,672,510 11,336,255 34,008,766 17,004,383 51,013,150 25,506,575 76,519,726 38,259,863 114,779,590 57,389,795 172,169,386 86,084,693 258,254,080 129,127,040 64,563,520 32,281,760 16,140,880 8,070,440 4,035,220 2,017,610 1,008,805 3,026,416 1,513,208 756,604 378,302 189,151 567,454 283,727 851,182 425,591 1,276,774 638,387 1,915,162 957,581 2,872,744 1,436,372 718,186 359,093 1,077,280 538,640 269,320 134,660 67,330 33,665 100,996 50,498 25,249 75,748 37,874 18,937 56,812 28,406 14,203 42,610 21,305 63,916

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