Factors that 42 room the list of hopeful and an unfavorable whole numbers that deserve to be split evenly into 42. Negative factors that 42 space just determinants with a negative sign. The number 42 is significant and is an also composite number which means that it has several factors, in this case, 42 has actually 8 factors. In this lesson, we will certainly calculate the factors of 42, its element factors, and its factors in pairs. We will certainly also try a few solved instances to know this topic better.
You are watching: Write 42 as a product of prime factors.
|1.||What are determinants of 42?|
|2.||How come Calculate determinants of 42?|
|3.||Factors the 42 by prime Factorization|
What are factors of 42?
Factors the a number are the number which divide the offered number exactly without leaving any type of remainder. Factors the 42 are 1, 2, 3, 6, 7, 14, 21 and also 42.
How to calculation the components of 42?
We deserve to use different methods prefer prime factorization and also the department method to calculation the components of 42. In element factorization, us express 42 together the product of its prime factors and in the department method, us look for numbers that divide 42 specifically without a remainder.
Factors that 42 by element Factorization
Prime factorization way expressing a number in regards to the product of its prime factors. We deserve to do this utilizing the department method or by making use of a variable tree.
Prime administrate by Division:Step 1: The number 42 is separated by the smallest prime number i m sorry divides 42 exactly, i.e. It pipeline a remainder 0.Step 2: The quotient is then split by the the smallest or 2nd smallest prime number and also the process continues it spins the quotient cannot be more divided.Step 3: Let united state divide 42 by the element number 2 i.e 42 ÷ 2 = 21.Step 4: Now we have to divide the quotient 21 by the next least prime number.Step 5: Since 21 is one odd number, that is no divisible by 2. Let us try dividing that by 3 i beg your pardon is 21 ÷ 3 = 7.Step 6: 7 is a element number and also we cannot division it further.Step 7: Therefore, the prime components of 42 space 2, 3, and also 7.
Prime administrate of 42 = 2 × 3 × 7
Prime administer by element Tree
Since we room finding the prime determinants of 42, they will be inserted as the root of our variable tree. Next, we compose a pair of determinants (two numbers, as soon as multiplied, give 42) as branches.
3 and also 7 space prime numbers and also at this point, the element tree ends. Let us express 42 in terms of the product that its element factors.42 = 2 × 3 × 7
Viola! We have actually done the element factorization. Here is a basic activity to shot on her own. Rather of 2 × 21, if we had actually used 6 × 7, perform you think we would gain the same factors? have the right to you draw the factor tree v 6 and also 7 together the branches?
Prime administer by Upside-Down Division
This technique is dubbed the upside-down division because the division symbol is flipped upside down. In this method, we divide 42 by the the smallest prime number 2 (if the number is odd, we start with 3). 7 is a prime number. It is divisible just by 7. We prevent the department when us reach 1.
Therefore, 42 deserve to be expressed together a product that its prime factors as 2 × 3 × 7. Explore factors utilizing illustrations and interactive examples:
Think Tank:8 × 21 ÷ 4 = 42, does this median 8 and 21 ÷ 4 are determinants of 42? Think!10.5 × 4 = 42, space 10.5 and also 4 factors of 42?Can a number better than 42 be its factor?
Factors the 42 in Pairs
Factor pairs room the two numbers which, once multiplied, give the number 42.1 × 42 = 422 × 21 = 423 × 14 = 426 × 7 = 42
Therefore, the pair components of 42 are (1,42), (2,21), (3,14), and also (6,7). Because the product that two an adverse numbers is positive, i.e. (-) × (-) = (+), the element pairs that 42 additionally include (-1,-42), (-2,-21), (-3,-14), and (-6,-7). Yet let us emphasis on the positive determinants in this lesson.
We divide 42 by herbal numbers and also see i m sorry numbers leave a remainder 0. The numbers which division 42 precisely without any kind of remainder room the factors of 42.
Division an approach to Find components of 42:
We watch that as soon as 42 is split by 1, 2, 3, 6, 7, 14, 21, and also 42, it pipeline no remainder. Hence, they are factors of 42.
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Important Notes:The number which us multiply to get 42 are the components of 42.Factors that 42 room 1, 2, 3, 6, 7, 14, 21, and 42.1 is a universal factor. The is a variable of every numbers. The number itself is a factor of the number as it divides itself exactly.Factor pairs space the pairs of two numbers which, as soon as multiplied, give the number. Variable pairs of 42 room (1, 42), (2, 21), (3,14), and also (6,7).