How to find the factors of 49
Test every whole number from 1 up to the square root of 49 (√49 ≈ 7.000). Each number that divides evenly gives you two factors at once: the divisor and the quotient.
- 49 ÷ 1 = 49 — so 1 and 49 are factors
- 49 ÷ 2 = 24.5 — not a whole number
- 49 ÷ 3 = 16.333 — not a whole number
- 49 ÷ 4 = 12.25 — not a whole number
- 49 ÷ 5 = 9.8 — not a whole number
- 49 ÷ 6 = 8.167 — not a whole number
- 49 ÷ 7 = 7 — so 7 and 7 are factors
Collecting both numbers from every successful division gives the complete list: 1, 7 and 49.
Prime factorization of 49
Divide by the smallest prime that fits, and keep going until the quotient is 1:
The primes you divided by give 49 = 7². From the exponents you can also count the factors without listing them: (2 + 1) = 3.
Properties of 49
- 49 is a composite number.
- The sum of all its factors is 57; the sum of its proper factors (excluding 49) is 8, which makes it a deficient number (its proper factors add up to less than itself).
- 49 is a perfect square: 7 × 7. Perfect squares always have an odd number of factors.
- Multiples of 49 include 98, 147, 196, 245 and so on.
Factors vs. multiples
Factors of 49 are the numbers that divide into it; multiples of 49 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.
Frequently asked questions
What are the factors of 49?
The factors of 49 are 1, 7 and 49. Each of these divides 49 with no remainder.
How many factors does 49 have?
49 has 3 positive factors, which form 2 factor pairs. Counting negative factors as well doubles that to 6.
What is the prime factorization of 49?
49 = 7². Its distinct prime factors are 7.
Is 49 a prime number?
No. 49 is composite because it has 3 factors, more than the two a prime number has.