Factors of 126

How to find the factors of 126

Test every whole number from 1 up to the square root of 126 (√126 ≈ 11.225). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 126 ÷ 1 = 126 — so 1 and 126 are factors
• 126 ÷ 2 = 63 — so 2 and 63 are factors
• 126 ÷ 3 = 42 — so 3 and 42 are factors
• 126 ÷ 4 = 31.5 — not a whole number
• 126 ÷ 5 = 25.2 — not a whole number
• 126 ÷ 6 = 21 — so 6 and 21 are factors
• 126 ÷ 7 = 18 — so 7 and 18 are factors
• 126 ÷ 8 = 15.75 — not a whole number
• 126 ÷ 9 = 14 — so 9 and 14 are factors
• 126 ÷ 10 = 12.6 — not a whole number
• 126 ÷ 11 = 11.455 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63 and 126.

Prime factorization of 126

Divide by the smallest prime that fits, and keep going until the quotient is 1:

The primes you divided by give 126 = 2 × 3² × 7. From the exponents you can also count the factors without listing them: (1 + 1) × (2 + 1) × (1 + 1) = 12.

Properties of 126

• 126 is a composite number.
• The sum of all its factors is 312; the sum of its proper factors (excluding 126) is 186, which makes it a abundant number (its proper factors add up to more than itself).
• 126 is not a perfect square, so its factors pair up evenly.
• Multiples of 126 include 252, 378, 504, 630 and so on.

Factors vs. multiples

Factors of 126 are the numbers that divide into it; multiples of 126 are the numbers it divides into. Every number has a limited set of factors but infinitely many multiples. To work with any other number, use the factors calculator, or find shared factors with the GCF calculator.