The divisors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The divisors of 36 are those numbers that completely divide 36 without a remainder. In this section, we will discuss divisors of 36.
Table of Contents
Highlights of Divisors of 36
- Divisors of 36: 1, 2, 3, 4, 6, 9, 12, 18 and 36
- Negative divisors of 36: -1, -2, -3, -4, -6, -9, -12, -18 and -36
- Prime divisors of 36: 2 and 3
- Number of divisors of 36: 9
- Sum of divisors of 36: 91
- Product of divisors of 36: 369/2 = 69
What are Divisors of 36
A number n is a divisor of 36 if $\frac{36}{n}$ is an integer. Note that if 36/n=m is an integer, then both m and n will be the divisors of 36.
To find the divisors of 36, we need to find the numbers n such that 36/n becomes an integer. We have:
| 36/1=36 | 1, 36 are divisors of 36. |
| 36/2=18 | 2, 18 are divisors of 36. |
| 36/3=12 | 3, 12 are divisors of 36 |
| 36/4=9 | 4, 9 are divisors of 36 |
| 36/6=6 | 6 is a divisor of 36 |
There are no numbers other than the above ones which can divide 36. Thus the divisors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. Thus, the total number of divisors of 36 is nine.
Video Solution of Divisors of 36
Negative Divisors of 36
Note that if m is a positive divisor of 36, then -m is a negative divisor of 36. As the divisors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36, we obtain that:
The negative divisors of 36 are -1, -2, -3, -4, -6, -9, -12, -18, and –36.
Prime Divisors of 36
The divisors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. Among these numbers, only 2 and 3 are prime numbers. So we obtain that:
The prime divisors of 36 are 2 and 3.
| Divisors of 48: The divisors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 |
| Divisors of 60: The divisors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 |
| Divisors of 72: The divisors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 |
| Divisors of 75: The divisors of 75 are 1, 3, 5, 15, 25, 75 |
Formulas of Divisors of 36
The prime factorization of 36 is given below.
36 = 22 × 32
(i) By the number of divisors formula, the number of divisors of 36 is
=(2+1)(2+1)=3×3=9.
(ii) By the sum of divisors formula, the sum of the divisors of 36 is
$=\frac{2^3-1}{2-1} \times \frac{3^3-1}{3-1}$
$=\frac{8-1}{1} \times \frac{27-1}{2}$
$=7 \times 13=91$
(iii) By the product of divisors formula, the product of the divisors of 36 is
=36(Number of divisors of 36)/2
=369/2
=69
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FAQs of Divisors of 36
Ans: The divisors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
Ans: As 1, 2, 3, 4, 6, 9, 12, 18, and 36 are the complete list of divisors of 36, we have that the total number of divisors of 36 is Nine.
Ans: The sum of divisors of 36 is equal to = (22 + 1 – 1)/(2 – 1) × (32 + 1 – 1)/(3 – 1) = 91
Ans: The product of divisors of 36 is = 36(Number of divisors of 36)/2 = 369/2 = 69
Ans: 2 and 3 are the prime divisors of 36.
Ans: The product of all the prime divisors of 36 = 2 × 3 = 6
