Question

A. List all the factors of 42 in ascending order:

b: List all the factors of 77 in ascending order:
c.List all the factors that are common to both 42 and 77:
d. List the greatest common factor of 42 and 77:
e: Fill in the blank: GCF(42,77) For parts
a.= and enter your answers as lists separated by commas and surrounded by parentheses_ For example the factors of 26 are (1,2,13,26).

Now prime factor 42 Enter your answers as lists separated by commas and surrounded by parentheses. Include duplicates.

Next, move every factor they have in common under the line_ Above the line write the lists that have not bccn movcd and bclow thc Iinc writc thc Uists that havc bccn movcd_ 42: 77: Enter your answers as lists separated by commas and surrounded by parentheses. Include duplicates. there are no numbers in your list, enter "DNE Finally , find the greatest common factor by multiplying what is below either of the two lines:

Answer 1

Explanation:

you need the factors, or the prime factors ? or both ?

it is not clear what you need, I will try to give you a much as possible for this topic, abd you will need to pick from there what you need.

it seems clear that we are dealing with 42 and 77.

let's start with prime factorization. you know what prime numbers are ? numbers that can only be divided without remainder by 1 and by itself. we always start with the smallest prime factor (2) and then work our way up until we get 1 as result :

42 ÷ 2 = 21

21 ÷ 2 no

21 ÷ 3 = 7

7 ÷ 3 no

7 ÷ 5 no

7 ÷ 7 = 1

finished

77 ÷ 2 no

77 ÷ 3 no

77 ÷ 5 no

77 ÷ 7 = 11

11 ÷ 7 no

11 ÷ 11 = 1

finished

so,

42 = 2×3×7

prime factors (2, 3, 7)

the factors are the prime factors and all possible combinations plus 1 and the number itself :

2×3 = 6

2×7 = 14

3×7 = 21

factors are (1, 2, 3, 6, 7, 14, 21, 42)

77 = 7×11

prime factors (7, 11)

there are no additional combinations.

factors are (1, 7, 11, 77)

the GCF is the product of the longest chains of prime factors they have in common.

the only prime factor chain 42 and 77 have in common is one time 7.

GCF (42, 77) = 7

FYI : there is also a thing called the smallest of least common multiple LCM. this is the smallest possible number that can be divided by both numbers without remainder.

it is the product of the longest chains of all prime factors in both numbers.

so, we have

LCM (42, 77) = 2×3×7×11 = 462