Divisors of 42

A number is said to be a divisor of 42 if that number completely divides 42 with the remainder zero. In this section, we will discuss about divisors of 42.

Highlights of Divisors of 42

• Divisors of 42: 1, 2, 3, 6, 7, 14, 21 and 42
• Negative divisors of 42: -1, -2, -3, -6, -7, -14, -21 and -42
• Prime divisors of 42: 2, 3 and 7
• Number of divisors of 42: 8
• Sum of divisors of 42: 96
• Product of divisors of 42: 42⁴

What are Divisors of 42

A number n is a divisor of 42 if $\dfrac{42}{n}$ is an integer. Note that if 42/n=m is an integer, then both m and n will be the divisors of 42.

To find the divisors of 42, we need to find the numbers n such that 42/n becomes an integer. We have:

42/1=42	1, 42 are divisors of 42.
42/2=21	2, 21 are divisors of 42
42/3=14	3, 14 are divisors of 42
42/6=7	6, 7 are divisors of 42

No numbers other than 1, 2, 3, 6, 7, 14, 21, and 42 can divide 42. So we conclude that

The divisors of 42 are: 1, 2, 3, 6, 7, 14, 21, and 42.

Thus, the total number of divisors of 42 is eight.

Negative Divisors of 42

We know that if m is a divisor of a number, then -m is also a divisor of that number.

As the divisors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42, we can say that:

The negative divisors of 42 are -1, -2, -3, -6, -7, -14, -21, and –42.

Prime Divisors of 42

The divisors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. Among these numbers, only 2, 3, and 7 are prime numbers. So we obtain that:

The prime divisors of 42 are 2, 3, and 7.

Video solution of Divisors of 42:

Sum, Product & Number of Divisors of 42

The prime factorization of 42 is given below.

42 = 2¹ × 3¹ ×7¹

(i) By the number of divisors formula, we have that the number of divisors of 42 is

=(1+1)(1+1)(1+1)=2×2×2=8.

(ii) By the sum of divisors formula, we have that the sum of the divisors of 42 is

$=\dfrac{2^2-1}{2-1}  \times \dfrac{3^2-1}{3-1} \times \dfrac{7^2-1}{7-1}$

$=\dfrac{4-1}{1} \times \dfrac{9-1}{2} \times \dfrac{49-1}{6}$

$=3 \times 4 \times 8=96$

(iii) By the product of divisors formula, we have that the product of the divisors of 42 is

=42^{(Number of divisors of 42)/2}

=42^8/2

=42⁴

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