Find numbers between 1 and 100 having exactly three factors. (2024)

FAQs

Find numbers between 1 and 100 having exactly three factors.? ›

Such numbers between 1 and 100 are 4,9,25 and 49. Was this answer helpful?

Only those numbers which are squares of prime numbers have exactly 3 factors. For example, 25 is the square of 5 (a prime number) and it has exactly 3 factors (1, 5 and 25). If p is a prime number, then p2 has exactly 3 factors viz. 1 , p and p2 .

How many factors of 3 will be in 100? Well, the integer factors of 3 are 1 and 3 as it's a prime number. There are 100 1′s and 33 3's, making 133.

The square of any prime number has exactly three factors. So, 4, 9, 25 and 49 have exactly three factors.

Such numbers between 1 and 100 are 4,9,25 and 49. Was this answer helpful?

The number 4 is the smallest positive integer that has exactly three factors: 1,2 and 4.

The natural numbers from 1 to 100 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, ...

Example 2: How many factors does 100 have? Solution: The factors of 100: 1, 2, 4, 5, 10, 20, 25, 50 and 100. So, there are 9 factors of 100.

Instant Answer

100 ÷ 3 = 33 with a remainder of 1. So, 3 goes into 100 a total of 33 times with a remainder of 1.

What number 1/100 has the most factors? ›

So there are 5 integers from 1 to 100 that have the most factors. they are 60, 72, 84, 90 & 96.

3 is not a composite number as it has exactly two factors. The factors of 3 are 1 and 3. This suggests that it is a prime number.

All numbers between 1 and 100 with four as a factor are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, and 96.

As the number 100 is an even composite number, 100 has many factors other than 1 and the number itself. Thus, the factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100. Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, and 100.

In other words, for a 3-digit number to have exactly three factors then it must be square of a prime number. So, the numbers are N =p^2 = 121, 169, 289, 529, 841 and 961. Since 3 is a prime the numbers are perfect squares of a prime. There are 11 such integers.

What are the Factors of 25? The factors of 25 are the numbers that divide 25 exactly without leaving any remainder. As 25 is a composite number, it has many factors other than 1 and 25. Thus, the factors of 25 are 1, 5 and 25.

A number has 3 divisors if it is a square of a prime number. For example 4 is a square of prime number 2. Here 4 has 3 divisors. 1,2,4.

There are zero factors of 20736 that have exactly 3 factors. A number can only have exactly three factors if its prime factorization includes only one prime number raised to a certain power. For instance, the prime factorization of 9 (3²) results in only two distinct factors (1 and 9).

25 and 49 are the only two digit numbers which will have exactly three factors. This is because a number will have three factor if and only if the number is a square of a prime number. So 25 and 49 are the only two digit numbers with exactly three factors.