The divisors of 100 are those numbers that completely divide 100 with the remainder zero. In this section, we will discuss about divisors of 100.
Highlights of Divisors of 100
- Divisors of 100: 1, 2, 4, 5, 10, 20, 25, 50 and 100
- Negative divisors of 100: -1 -2, -4, -5, -10, -20, -25, -50 and -100
- Prime divisors of 100: 2 and 5
- Number of divisors of 100: 9
- Sum of divisors of 100: 217
- Product of divisors of 100: 1009/2 = 109
What are Divisors of 100
A number n is a divisor of 100 if $\dfrac{100}{n}$ is an integer. Note that if 100/n=m is an integer, then both m and n will be the divisors of 100.
To find the divisors of 100, we need to find the number n such that 100/n becomes an integer. We have:
100/1=100 | 1, 100 are divisors of 100. |
100/2=50 | 2, 50 are divisors of 100 |
100/4=25 | 4, 25 are divisors of 100 |
100/5=20 | 5, 20 are divisors of 100 |
100/10=10 | 10 is a divisor of 100 |
No numbers other than 1, 2, 4, 5, 10, 20, 25, 50, and 100 can divide 100. So we conclude that
The divisors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50, and 100. |
Thus, the total number of divisors of 100 is nine.
Also Read:
Divisors of 60: | The divisors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. |
Divisors of 64: | The divisors of 64 are 1, 2, 4, 8, 16, 32, 64. |
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. |
Negative Divisors of 100
We know that if m is a divisor of a number, then -m is also a divisor of that number.
As the divisors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100, we can say that:
The negative divisors of 100 are -1, -2, -4, -5, -10, -20, -25, -50, and -100.
Prime Divisors of 100
The divisors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100. Among these numbers, only 2 and 5 are prime numbers. So we obtain that:
The prime divisors of 100 are 2 and 5.
Sum, Product & Number of Divisors of 100
The prime factorization of 100 is given below.
100 = 22 × 52
(i) By the number of divisors formula, we have that the number of divisors of 100 is
=(2+1)(2+1)=3×3=9.
(ii) By the sum of divisors formula, we have that the sum of the divisors of 100 is
$=\dfrac{2^3-1}{2-1} \times \dfrac{5^3-1}{5-1}$
$=\dfrac{8-1}{1} \times \dfrac{125-1}{4}$
$=7 \times 31=217$
(iii) By the product of divisors formula, we have that the product of the divisors of 100 is
=100(Number of divisors of 100)/2
=1009/2
=109
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Question-Answer on Divisors of 100
Question 1: Find the highest divisor of 100.
Answer:
100 is the highest divisor of 100.
Question 2: Find the sum and the product of the divisors of 100.
Answer:
We know that the divisors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100. So the sum of the divisors of 100 is
= 1+2+4+5+10+20+25+50+100
= 217.
We know that the formula for the product of the divisors of N is as follows:
Product of divisors of N = NNo. of divisors of N |
As 100 has 9 divisors, we obtain that the product of the divisors of 100 is equal to 109.