Factors of 168

How to find the factors of 168

Test every whole number from 1 up to the square root of 168 (√168 ≈ 12.961). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 168 ÷ 1 = 168 — so 1 and 168 are factors
• 168 ÷ 2 = 84 — so 2 and 84 are factors
• 168 ÷ 3 = 56 — so 3 and 56 are factors
• 168 ÷ 4 = 42 — so 4 and 42 are factors
• 168 ÷ 5 = 33.6 — not a whole number
• 168 ÷ 6 = 28 — so 6 and 28 are factors
• 168 ÷ 7 = 24 — so 7 and 24 are factors
• 168 ÷ 8 = 21 — so 8 and 21 are factors
• 168 ÷ 9 = 18.667 — not a whole number
• 168 ÷ 10 = 16.8 — not a whole number
• 168 ÷ 11 = 15.273 — not a whole number
• 168 ÷ 12 = 14 — so 12 and 14 are factors

Collecting both numbers from every successful division gives the complete list: 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84 and 168.

Prime factorization of 168

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

The primes you divided by give 168 = 2³ × 3 × 7. From the exponents you can also count the factors without listing them: (3 + 1) × (1 + 1) × (1 + 1) = 16.

Properties of 168

• 168 is a composite number.
• The sum of all its factors is 480; the sum of its proper factors (excluding 168) is 312, which makes it a abundant number (its proper factors add up to more than itself).
• 168 is not a perfect square, so its factors pair up evenly.
• Multiples of 168 include 336, 504, 672, 840 and so on.

Factors vs. multiples

Factors of 168 are the numbers that divide into it; multiples of 168 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.