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Atlas › Integer Profiles › Node 76,449,472

76,449,472

26 × 11 × 312 × 113
Abundant Even Composite

76,449,472 factors as 2^6 × 11 × 31^2 × 113. Its 84 positive divisors give a proper-divisor sum of 96,070,376, so this integer is abundant. The Collatz stopping time is 197 steps.

Prime Factor Structure

Factorization String 2^6 × 11 × 31^2 × 113
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 84
Divisor Sum (σ) 172,519,848
Proper Divisor Sum 96,070,376
Digit Sum / Digital Root 43 (Root: 7)
Adjacent Primes #76449449 ← → #76449473

Radix Representation

Decimal 76449472
Binary 100100011101000011011000000 (27 bits)
Octal 0o443503300
Hexadecimal 0x48E86C0

Divisor Catalog (60 of 84)

1 2 4 8 11 16 22 31 32 44 62 64 88 113 124 176 226 248 341 352 452 496 682 704 904 961 992 1,243 1,364 1,808 1,922 1,984 2,486 2,728 3,503 3,616 3,844 4,972 5,456 7,006 7,232 7,688 9,944 10,571 10,912 14,012 15,376 19,888 21,142 21,824 28,024 30,752 38,533 39,776 42,284 56,048 61,504 77,066 79,552 84,568

Collatz Trajectory (197 steps to reach 1)

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

76,449,472 38,224,736 19,112,368 9,556,184 4,778,092 2,389,046 1,194,523 3,583,570 1,791,785 5,375,356 2,687,678 1,343,839 4,031,518 2,015,759 6,047,278 3,023,639 9,070,918 4,535,459 13,606,378 6,803,189 20,409,568 10,204,784 5,102,392 2,551,196 1,275,598 637,799 1,913,398 956,699 2,870,098 1,435,049 4,305,148 2,152,574 1,076,287 3,228,862 1,614,431 4,843,294 2,421,647 7,264,942 3,632,471 10,897,414 5,448,707 16,346,122 8,173,061 24,519,184 12,259,592 6,129,796 3,064,898 1,532,449 4,597,348 2,298,674 1,149,337 3,448,012 1,724,006 862,003 2,586,010 1,293,005 3,879,016 1,939,508 969,754 484,877

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