Factors of 42 are the list of positive and negative whole numbers that can be divided evenly into 42. Negative factors of 42 are just factors with a negative sign. The number 42 is significant and is an even composite number which means that it has several factors, in this case, 42 has 8 factors. In this lesson, we will calculate the factors of 42, its prime factors, and its factors in pairs. We will also try a few solved examples to understand this topic better.
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|1.||What are Factors of 42?|
|2.||How to Calculate Factors of 42?|
|3.||Factors of 42 by Prime Factorization|
What are Factors of 42?
Factors of a number are the numbers which divide the given number exactly without leaving any remainder. Factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42.
How to Calculate the Factors of 42?
We can use different methods like prime factorization and the division method to calculate the factors of 42. In prime factorization, we express 42 as the product of its prime factors and in the division method, we look for numbers that divide 42 exactly without a remainder.
Factors of 42 by Prime Factorization
Prime factorization means expressing a number in terms of the product of its prime factors. We can do this using the division method or by using a factor tree.
Prime Factorization by Division:Step 1: The number 42 is divided by the smallest prime number which divides 42 exactly, i.e. it leaves a remainder 0.Step 2: The quotient is then divided by the smallest or second smallest prime number and the process continues till the quotient cannot be further divided.Step 3: Let us divide 42 by the prime number 2 i.e 42 ÷ 2 = 21.Step 4: Now we need to divide the quotient 21 by the next least prime number.Step 5: Since 21 is an odd number, it is not divisible by 2. Let us try dividing it by 3 which is 21 ÷ 3 = 7.Step 6: 7 is a prime number and we cannot divide it further.Step 7: Therefore, the prime factors of 42 are 2, 3, and 7.
Prime factorization of 42 = 2 × 3 × 7
Prime Factorization by Factor Tree
Since we are finding the prime factors of 42, they will be placed as the roots of our factor tree. Next, we write a pair of factors (two numbers, when multiplied, give 42) as branches.
3 and 7 are prime numbers and at this point, the factor tree ends. Let us express 42 in terms of the product of its prime factors.42 = 2 × 3 × 7
Viola! We have done the prime factorization. Here is a simple activity to try on your own. Instead of 2 × 21, if we had used 6 × 7, do you think we would get the same factors? Can you draw the factor tree with 6 and 7 as the branches?
Prime Factorization by Upside-Down Division
This method is called the upside-down division because the division symbol is flipped upside down. In this method, we divide 42 by the smallest prime number 2 (if the number is odd, we start with 3). 7 is a prime number. It is divisible only by 7. We stop the division when we reach 1.
Therefore, 42 can be expressed as a product of its prime factors as 2 × 3 × 7. Explore factors using illustrations and interactive examples:
Think Tank:8 × 21 ÷ 4 = 42, does this mean 8 and 21 ÷ 4 are factors of 42? Think!10.5 × 4 = 42, are 10.5 and 4 factors of 42?Can a number greater than 42 be its factor?
Factors of 42 in Pairs
Factor pairs are the two numbers which, when multiplied, give the number 42.1 × 42 = 422 × 21 = 423 × 14 = 426 × 7 = 42
Therefore, the pair factors of 42 are (1,42), (2,21), (3,14), and (6,7). Since the product of two negative numbers is positive, i.e. (-) × (-) = (+), the factor pairs of 42 also include (-1,-42), (-2,-21), (-3,-14), and (-6,-7). But let us focus on the positive factors in this lesson.
We divide 42 by natural numbers and see which numbers leave a remainder 0. The numbers which divide 42 exactly without any remainder are the factors of 42.
Division Method to Find Factors of 42:
We see that when 42 is divided by 1, 2, 3, 6, 7, 14, 21, and 42, it leaves no remainder. Hence, they are factors of 42.
See more: What Does The Acronym Acd Stand For? ? What Does Acd Stand For
Important Notes:The numbers which we multiply to get 42 are the factors of 42.Factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.1 is a universal factor. It is a factor of all numbers. The number itself is a factor of the number as it divides itself exactly.Factor pairs are the pairs of two numbers which, when multiplied, give the number. Factor pairs of 42 are (1, 42), (2, 21), (3,14), and (6,7).