Divisors of 7744: All 21 Factors

Divisors (Factors) Calculator

Use the calculator above to find all divisors (also called factors) of any positive integer up to 4,782,969. Beyond the divisor list, this tool also shows divisor pairs, the sum and count of divisors, prime factorization, and number properties (prime, perfect square, perfect number).

All Divisors of 7744

The number 7744 has 21 divisors:

1,  2,  4,  8,  11,  16,  22,  32,  44,  64,  88,  121,  176,  242,  352,  484,  704,  968,  1936,  3872,  7744

Divisor Pairs of 7744

Each pair multiplies to 7744:

Note: the last pair has identical factors (88 × 88) because 7744 is a perfect square.

Number of Divisors

The number 7744 has 21 divisors, written as τ(7744) = 21 in number theory.

⚡ Notice: 7744 has an odd number of divisors — this means 7744 is a perfect square (√7744 = 88).

Sum of Divisors

σ(7744) = 1 + 2 + 4 + 8 + 11 + 16 + 22 + 32 + 44 + 64 + 88 + 121 + 176 + 242 + 352 + 484 + 704 + 968 + 1936 + 3872 + 7744 = 16891

Prime Factorization of 7744

See the full prime factorization calculator →

Properties of 7744

• 7744 is composite.
• 7744 is a perfect square (√7744 = 88).
• Number of divisors: 21.
• Sum of divisors: 16891.

Common Divisors with Another Number?

Looking for the divisors that 7744 shares with another number? Use our Greatest Common Factor (GCF) calculator — it finds all common divisors and the largest one.

Step-by-Step: How to Find the Divisors of 7744

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √7744 ≈ 88.00. If i divides 7744, then both i and 7744/i are divisors.

1. 1 divides 7744 (7744 ÷ 1 = 7744) → pair (1, 7744)
2. 2 divides 7744 (7744 ÷ 2 = 3872) → pair (2, 3872)
3. 4 divides 7744 (7744 ÷ 4 = 1936) → pair (4, 1936)
4. 8 divides 7744 (7744 ÷ 8 = 968) → pair (8, 968)
5. 11 divides 7744 (7744 ÷ 11 = 704) → pair (11, 704)
6. 16 divides 7744 (7744 ÷ 16 = 484) → pair (16, 484)
7. 22 divides 7744 (7744 ÷ 22 = 352) → pair (22, 352)
8. 32 divides 7744 (7744 ÷ 32 = 242) → pair (32, 242)
9. 44 divides 7744 (7744 ÷ 44 = 176) → pair (44, 176)
10. 64 divides 7744 (7744 ÷ 64 = 121) → pair (64, 121)
11. 88 divides 7744 (7744 ÷ 88 = 88) → pair (88, 88)
12. Collect all unique values: {1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 121, 176, 242, 352, 484, 704, 968, 1936, 3872, 7744} — total 21 divisors.
13. Sum: 1 + 2 + 4 + 8 + 11 + 16 + 22 + 32 + 44 + 64 + 88 + 121 + 176 + 242 + 352 + 484 + 704 + 968 + 1936 + 3872 + 7744 = 16891.

Nearby Examples

Related Operations for 7744

• Multiples of 7744 — "outward" complement; M is a multiple of 7744 ⇔ 7744 is a divisor of M
• 7744 Prime Factorization — decompose into prime building blocks
• Find GCF of 7744 and another number
• Find LCM of 7744 and another number
• Is 7744 a perfect square? (odd divisor count ⇔ yes)

See also our tables of divisors:

• Table of all divisors from 1 to 100
• Table of all divisors from 1 to 500
• Table of all divisors from 1 to 1,000
• Table of all divisors from 1 to 10,000

What Is a Divisor?

A divisor (also called a factor) of a positive integer n is any positive integer d such that n ÷ d has no remainder. In other words, d divides n evenly.

Every positive integer n has at least two divisors: 1 and n itself (with 1 being the trivial case of having only itself). Numbers with exactly 2 divisors are prime; numbers with 3 or more divisors are composite.

Why use this calculator? Beyond just listing divisors, this tool computes the sum σ(n), the count τ(n), prime factorization, divisor pairs (useful for visual learners and factoring problems), and detects whether n is a prime, a perfect square, or a perfect number.

References

• [1] Divisor (Wikipedia)
• [2] Divisor function (Wikipedia)
• [3] Divisor (Wolfram MathWorld)

Divisors Calculation Examples

Find all divisors of these numbers: