Divisors of 742: All 8 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 742

The number 742 has 8 divisors:

1,  2,  7,  14,  53,  106,  371,  742

Divisor Pairs of 742

Each pair multiplies to 742:

Number of Divisors

The number 742 has 8 divisors, written as τ(742) = 8 in number theory.

Sum of Divisors

σ(742) = 1 + 2 + 7 + 14 + 53 + 106 + 371 + 742 = 1296

Prime Factorization of 742

See the full prime factorization calculator →

Properties of 742

• 742 is composite.
• 742 is not a perfect square.
• Number of divisors: 8.
• Sum of divisors: 1296.

Common Divisors with Another Number?

Looking for the divisors that 742 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 742

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √742 ≈ 27.24. If i divides 742, then both i and 742/i are divisors.

1. 1 divides 742 (742 ÷ 1 = 742) → pair (1, 742)
2. 2 divides 742 (742 ÷ 2 = 371) → pair (2, 371)
3. 7 divides 742 (742 ÷ 7 = 106) → pair (7, 106)
4. 14 divides 742 (742 ÷ 14 = 53) → pair (14, 53)
5. Collect all unique values: {1, 2, 7, 14, 53, 106, 371, 742} — total 8 divisors.
6. Sum: 1 + 2 + 7 + 14 + 53 + 106 + 371 + 742 = 1296.

Nearby Examples

Related Operations for 742

• Multiples of 742 — "outward" complement; M is a multiple of 742 ⇔ 742 is a divisor of M
• 742 Prime Factorization — decompose into prime building blocks
• Find GCF of 742 and another number
• Find LCM of 742 and another number
• Is 742 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

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