# Divisors example sentences

**Related** (2): Factors, multiples

## di·vi·sor

[dəˈvīzər] ✕ Play

divisors (plural noun)

- a number by which another number is to be divided.

- a number that divides into another without a remainder:

### Synonyms

Wikipedia### "Divisors" Example Sentences

1. Five has two divisors: 1 and 5.2. The number 14 has four divisors: 1, 2, 7, and 14.

3. A prime number only has two divisors: 1 and itself.

4. The divisors of 20 are 1, 2, 4, 5, 10, and 20.

5. The product of all the divisors of 12 is 1296.

6. The sum of all the divisors of 36 is 91.

7. The number 36 is a perfect square because it has an odd number of divisors.

8. The prime factorization of 72 is 2^3 x 3^2, so it has (3+1)(2+1) = 12 divisors.

9. The divisors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.

10. The number 45 has four divisors that are odd: 1, 3, 5, and 15.

11. A number with an odd number of divisors is a perfect square.

12. The divisors of a prime number are only 1 and itself.

13. The number 18 has six divisors: 1, 2, 3, 6, 9, and 18.

14. A divisor of a number must be less than or equal to the number itself.

15. The divisors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300.

16. The number 24 has eight divisors because its prime factorization is 2^3 x 3^1: (3+1)(1+1) = 8.

17. Every positive integer has at least two divisors: the number 1 and itself.

18. A number that has exactly three divisors is called a square-free number.

19. The sum of the divisors of a perfect number is always equal to twice the number itself.

20. The only positive integer that has exactly one divisor is 1.

21. The divisors of a number are always in pairs, except for square numbers.

22. A number is prime if and only if it has exactly two divisors.

23. The divisors of 16 are 1, 2, 4, 8, and 16.

24. A divisor of a number is a factor that evenly divides the number without leaving a remainder.

25. The number 27 has four divisors: 1, 3, 9, and 27.

26. The number 10 has four divisors: 1, 2, 5, and 10.

27. The smallest number with exactly 10 divisors is 48.

28. A divisor of a number cannot be greater than half the number itself.

29. The product of two consecutive integers is always divisible by 2 and has exactly three divisors.

30. A number is perfect if and only if the sum of its proper divisors is equal to the number itself.

### Common Phases

1. Finding all the divisors of a number2. Checking if a number is divisible by another

3. Prime factorization with divisors

4. Writing a number as a product of its divisors

5. Using the greatest common divisor to simplify fractions

6. Finding the least common multiple using divisors

7. Proving a number is prime by checking its divisors

8. Using the Euclidean algorithm to find the GCD and LCM of two numbers

9. Proving two numbers are coprime by analyzing their divisors

10. Dividing a number by a divisor to find the quotient and remainder.

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