Question

question 4 of 5
all of the following answer choices are factors of 777 except:
a 1
b 3
c 17
d 21

Explanation:

Step1: Recall the definition of a factor

A factor of a number \( n \) is an integer that divides \( n \) without leaving a remainder. So we need to check which of the given options does not divide 777 evenly.

Step2: Check option A (1)

Any number is divisible by 1. So \( 777\div1 = 777 \) with remainder 0. So 1 is a factor.

Step3: Check option B (3)

To check divisibility by 3, we can use the rule that if the sum of the digits of a number is divisible by 3, the number is divisible by 3. The sum of digits of 777 is \( 7 + 7+ 7=21 \), and \( 21\div3 = 7 \), so 21 is divisible by 3, hence 777 is divisible by 3. \( 777\div3=259 \) with remainder 0. So 3 is a factor.

Step4: Check option C (17)

Divide 777 by 17: \( 777\div17 = 45.705\cdots \) (we can also do long division: \( 17\times45 = 765 \), \( 777 - 765=12 \)), so there is a remainder of 12. So 17 does not divide 777 evenly.

Step5: Check option D (21)

We can factorize 777: \( 777=3\times259 = 3\times7\times37 \). Also, \( 21 = 3\times7 \), so \( 777\div21=\frac{777}{21} = 37 \) with remainder 0. So 21 is a factor.

Answer:

C. 17