Factors of 196

How to find the factors of 196

Test every whole number from 1 up to the square root of 196 (√196 ≈ 14.000). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 196 ÷ 1 = 196 — so 1 and 196 are factors
• 196 ÷ 2 = 98 — so 2 and 98 are factors
• 196 ÷ 3 = 65.333 — not a whole number
• 196 ÷ 4 = 49 — so 4 and 49 are factors
• 196 ÷ 5 = 39.2 — not a whole number
• 196 ÷ 6 = 32.667 — not a whole number
• 196 ÷ 7 = 28 — so 7 and 28 are factors
• 196 ÷ 8 = 24.5 — not a whole number
• 196 ÷ 9 = 21.778 — not a whole number
• 196 ÷ 10 = 19.6 — not a whole number
• 196 ÷ 11 = 17.818 — not a whole number
• 196 ÷ 12 = 16.333 — not a whole number
• 196 ÷ 13 = 15.077 — not a whole number
• 196 ÷ 14 = 14 — so 14 and 14 are factors

Collecting both numbers from every successful division gives the complete list: 1, 2, 4, 7, 14, 28, 49, 98 and 196.

Prime factorization of 196

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

The primes you divided by give 196 = 2² × 7². From the exponents you can also count the factors without listing them: (2 + 1) × (2 + 1) = 9.

Properties of 196

• 196 is a composite number.
• The sum of all its factors is 399; the sum of its proper factors (excluding 196) is 203, which makes it a abundant number (its proper factors add up to more than itself).
• 196 is a perfect square: 14 × 14. Perfect squares always have an odd number of factors.
• Multiples of 196 include 392, 588, 784, 980 and so on.

Factors vs. multiples

Factors of 196 are the numbers that divide into it; multiples of 196 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.