Factors of 138

How to find the factors of 138

Test every whole number from 1 up to the square root of 138 (√138 ≈ 11.747). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 138 ÷ 1 = 138 — so 1 and 138 are factors
• 138 ÷ 2 = 69 — so 2 and 69 are factors
• 138 ÷ 3 = 46 — so 3 and 46 are factors
• 138 ÷ 4 = 34.5 — not a whole number
• 138 ÷ 5 = 27.6 — not a whole number
• 138 ÷ 6 = 23 — so 6 and 23 are factors
• 138 ÷ 7 = 19.714 — not a whole number
• 138 ÷ 8 = 17.25 — not a whole number
• 138 ÷ 9 = 15.333 — not a whole number
• 138 ÷ 10 = 13.8 — not a whole number
• 138 ÷ 11 = 12.545 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 2, 3, 6, 23, 46, 69 and 138.

Prime factorization of 138

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

The primes you divided by give 138 = 2 × 3 × 23. From the exponents you can also count the factors without listing them: (1 + 1) × (1 + 1) × (1 + 1) = 8.

Properties of 138

• 138 is a composite number.
• The sum of all its factors is 288; the sum of its proper factors (excluding 138) is 150, which makes it a abundant number (its proper factors add up to more than itself).
• 138 is not a perfect square, so its factors pair up evenly.
• Multiples of 138 include 276, 414, 552, 690 and so on.

Factors vs. multiples

Factors of 138 are the numbers that divide into it; multiples of 138 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.