Factors of 72
All the integers (positive or negative), which given remainder zero on the division of 72, are known as the factors of 72.
Factors of 72 are also called as the divisors of 72.
Factors Pairs of 72
When two factors of 72 are multiplied together, then both the numbers are called as the factors of 72.
Since
1 × 72 = 72
2 × 36 = 72
3 × 24 = 72
4 × 72 = 72
6 × 12 = 72
8 × 9 = 72
Thus, the factors pairs of 72 are
(1 and 72),
(2 and 36),
(3 and 24),
(4 and 18),
(6 and 12),
(8 and 9),
Positive and Negative Factors of 72
The positive factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
The negative factors of 72 are –1, –2, –3, –4, –6, –8, –9, –12, –18, –24, –36, –72.
Is 72 a Prime Number?
A prime number has only two factors, 1 and itself the number 72. But, the number of factors of 72 are more than two. Thus, 72 is not a prime number.
How to Find Factors of 72?
To find the factors of 72, you need to divide 72 by every natural numbers till 72 that completely divided 72
72 ÷ 1 = 72, so 1 is a factor of 72.
72 ÷ 2 = 36, so 2 is a factor of 72.
72 ÷ 3 = 24, so 3 is a factor of 72.
72 ÷ 4 = 18, so 4 is a factor of 72.
72 ÷ 6 = 12, so 6 is a factor of 72.
72 ÷ 8 = 9, so 8 is a factor of 72.
72 ÷ 9 = 8, so 9 is a factor of 72.
72 ÷ 12 = 6, so 12 is a factor of 72.
72 ÷ 18 = 4, so 18 is a factor of 72.
72 ÷ 24 = 3, so 24 is a factor of 72.
72 ÷ 36 = 2, so 36 is a factor of 72.
72 ÷ 72 = 1, so 72 is a factor of 72.
Thus, the factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
How many Factors of 72?
On counting the factors of 72, you get that the number of factors of 72 are 12.
Prime Factors of 72?
The prime factor of 72 is a number, which is divisible by 1 and itself.
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
In the factors of 72, Since 2 and 3 are prime numbers, then the prime factors of 72 are 2 and 3 only.
How many Prime Factors of 72?
There are two prime factors of 72, which are 2 and 3.
Prime Factorization of 72
There is exactly one prime factorization for any given number. The prime factorization of 72 is the list of prime numbers whose product is 72.
The prime factorization of 72 is 72 = 23 × 33.
How to calculate Prime Factorization of 72
To calculate a prime factorization of a number, divide 72 by prime factors of 72 continuously till get the quotient 1.
Step 1: Divide 72 by 2.
72 ÷ 2 = 36
Step 2: Again divide 36 by 2.
36 ÷ 2 = 18
Step 3: Again divide 18 by 2.
18 ÷ 2 = 9
Step 4: Now, 9 is not divisible by 2, you need to divided 9 by next prime factors of 72 that is 3.
9 ÷ 3 = 3
Step 5: Again divide 3 by 3.
3 ÷ 3 = 1
Now, you get the quotient 1 then stop.
Thus, the prime factorization of 72 is
72 = 2 × 2 × 2 × 3 × 3 = 23 × 32.
How to find all Factors of 72 by Prime Factorization
Since the prime factorization of 72 is 72 = 23 × 32, then the factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
1 × 1 = 1,
1 × 2 = 2,
1 × 3 = 3
2 × 2 = 4,
2 × 3 = 6,
2 × 2 × 2 = 8
3 × 3 = 9
2 × 2 × 3 = 12
2 × 3 × 3 = 18
2 × 2 × 2 × 3 = 24
2 × 2 × 3 × 3 = 36
2 × 2 × 2 × 3 × 3 = 72
Factors of 6 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
Is 72 a Rational Number?
A number, that can be written in the form of p/q, where q ≠ 0, then the number is called as rational number. Since 72 / 1 = p / q, then YES, 72 is rational number.
Is 72 a Composite Number?
Since 72 is divisible by 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 then it is not prime. A number which is not prime is known as composite number. Thus, 72 is a composite number.
Is 72 a Perfect Square?
The prime factorization of 72 is 72 = 2 × 22 × 32. Since 2 is not in pair, so 72 is not a perfect square.
Is 72 a Perfect Cube?
The prime factorization of 72 is 72 = 23 × 32. Since 3 is not in triplet, so 72 is not a perfect Cube.
Write the First 10 Multiples of 72.
The first 10 multiples of 72 are
1 × 72 = 72,
2 × 72 = 144,
3 × 72 = 216
4 × 72 = 288
5 × 72 = 360
6 × 72 = 432
7 × 72 = 504
8 × 72 = 576
9 × 72 = 648
10 × 72 = 720
FAQs About the Number 72
Is 72 divisible by 6?
Since the prime factorization of 72 is 72 = 23 × 32 = (2 × 3) × 22 × 31 = (6) × 22 × 31 = 6 × 12
⇒ 72 is multiple of 6 and 72 / 6 = 12.
Thus, YES, 72 is divisible by 6.
Is 72 divisible by 3?
Since the prime factorization of 72 is 72 = 23 × 32 = (3) × 23 × 31 = 3 × 24
⇒ 72 is multiple of 3 and 72 / 3 = 24.
Thus, YES, 72 is divisible by 3.
Is 72 divisible by 9?
Since the prime factorization of 72 is 72 = 23 × 32 = (32) × 23 = 9 × 8
⇒ 72 is multiple of 9 and 72 / 9 = 8.
Thus, YES, 72 is divisible by 9.
Is 72 divisible by 2?
Since the prime factorization of 72 is 72 = 23 × 32 = (21) × 22 × 32 = 2 × 36
⇒ 72 is multiple of 2 and 72 / 2 = 36.
Thus, YES, 72 is divisible by 2.
Is 72 divisible by 4?
Since the prime factorization of 72 is 72 = 23 × 32 = (22) × 21 × 32 = 4 × 18
⇒ 72 is multiple of 4 and 72 / 4 = 18.
Thus, YES, 72 is divisible by 4.
Is 72 divisible by 18?
Since the prime factorization of 72 is 72 = 23 × 32 = (21 × 32) × 22 = 18 × 4
⇒ 72 is multiple of 18 and 72 / 18 = 4.
Thus, YES, 72 is divisible by 18.
Is 72 divisible by 16?
Since the prime factorization of 72 is 72 = 23 × 32 = (23) × 32 = 8 × 9
⇒ 72 is NOT a multiple of 16 and when 72 is divided by 16, there is a remainder of 8.
Thus, NO, 72 is NOT divisible by 16.
Is 72 divisible by 5?
Since the prime factorization of 72 is 72 = 23 × 32 = (23) × 32 = 8 × 9
⇒ 72 is NOT a multiple of 5 and when 72 is divided by 5, there is a remainder of 2.
Thus, NO, 72 is NOT divisible by 5.
Is 72 divisible by 8?
Since the prime factorization of 72 is 72 = 23 × 32 = (23) × 32 = 8 × 9
⇒ 72 is multiple of 8 and 72 / 8 = 9.
Thus, YES, 72 is divisible by 8.
Is 72 divisible by 7?
Since the prime factorization of 72 is 72 = 23 × 32 = (23) × 32 = 8 × 9
⇒ 72 is NOT a multiple of 7 and when 72 is divided by 7, there is a remainder of 2.
Thus, NO, 72 is NOT divisible by 7.
