Solved on Nov 17, 2023

Is $8,397$ divisible by $9$ ? If so, express it as $9 \times$ another factor. If not, explain.

STEP 1

Assumptions1. The number in question is8,397. We are checking if it is divisible by9

STEP 2

To check if a number is divisible by9, we can use the rule of9. The rule of9 states that a number is divisible by9 if the sum of its digits is divisible by9.

STEP 3

First, we need to find the sum of the digits of8,397.
$Sum\, of\, digits =8 +3 +9 +7$

STEP 4

Calculate the sum of the digits.
$Sum\, of\, digits =8 +3 +9 +7 =27$

STEP 5

Now, we need to check if the sum of the digits (27) is divisible by9.

STEP 6

Calculate the remainder when27 is divided by9.
$Remainder =27 \mod9$

STEP 7

Calculate the remainder.
$Remainder =27 \mod9 =0$

STEP 8

Since the remainder is0, the sum of the digits (27) is divisible by. Therefore, the original number (8,397) is also divisible by.

STEP 9

Now, we need to write8,397 as the product of9 and another factor. We can do this by dividing8,397 by9.
$Factor =8,397 /9$

STEP 10

Calculate the factor.
$Factor =8,397 /9 =933$ So,8,397 can be written as the product of9 and933.

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Is $8,397$ divisible by $9$ ? If so, express it as $9 \times$ another factor. If not, explain.

STEP 1

Assumptions1. The number in question is8,397. We are checking if it is divisible by9

STEP 2

To check if a number is divisible by9, we can use the rule of9. The rule of9 states that a number is divisible by9 if the sum of its digits is divisible by9.

STEP 3

First, we need to find the sum of the digits of8,397.
$Sum\, of\, digits =8 +3 +9 +7$

STEP 4

Calculate the sum of the digits.
$Sum\, of\, digits =8 +3 +9 +7 =27$

STEP 5

Now, we need to check if the sum of the digits (27) is divisible by9.

STEP 6

Calculate the remainder when27 is divided by9.
$Remainder =27 \mod9$

STEP 7

Calculate the remainder.
$Remainder =27 \mod9 =0$

STEP 8

Since the remainder is0, the sum of the digits (27) is divisible by. Therefore, the original number (8,397) is also divisible by.

STEP 9

Now, we need to write8,397 as the product of9 and another factor. We can do this by dividing8,397 by9.
$Factor =8,397 /9$

STEP 10

Calculate the factor.
$Factor =8,397 /9 =933$ So,8,397 can be written as the product of9 and933.

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Is 8,3978,3978,397 divisible by 999? If so, express it as 9×9 \times9× another factor. If not, explain.

STEP 1

Assumptions1. The number in question is8,397. We are checking if it is divisible by9

STEP 2

To check if a number is divisible by9, we can use the rule of9. The rule of9 states that a number is divisible by9 if the sum of its digits is divisible by9.

STEP 3

First, we need to find the sum of the digits of8,397.Sum of digits=8+3+9+7Sum\, of\, digits =8 +3 +9 +7Sumofdigits=8+3+9+7

STEP 4

Calculate the sum of the digits.Sum of digits=8+3+9+7=27Sum\, of\, digits =8 +3 +9 +7 =27Sumofdigits=8+3+9+7=27

STEP 5

Now, we need to check if the sum of the digits (27) is divisible by9.

STEP 6

Calculate the remainder when27 is divided by9.Remainder=27mod 9Remainder =27 \mod9Remainder=27mod9

STEP 7

Calculate the remainder.Remainder=27mod 9=0Remainder =27 \mod9 =0Remainder=27mod9=0

STEP 8

Since the remainder is0, the sum of the digits (27) is divisible by. Therefore, the original number (8,397) is also divisible by.

STEP 9

Now, we need to write8,397 as the product of9 and another factor. We can do this by dividing8,397 by9.Factor=8,397/9Factor =8,397 /9Factor=8,397/9

STEP 10

Calculate the factor.Factor=8,397/9=933Factor =8,397 /9 =933Factor=8,397/9=933So,8,397 can be written as the product of9 and933.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Is $8,397$ divisible by $9$ ? If so, express it as $9 \times$ another factor. If not, explain.

First, we need to find the sum of the digits of8,397.
$Sum\, of\, digits =8 +3 +9 +7$

Calculate the sum of the digits.
$Sum\, of\, digits =8 +3 +9 +7 =27$

Calculate the remainder when27 is divided by9.
$Remainder =27 \mod9$

Calculate the remainder.
$Remainder =27 \mod9 =0$

Now, we need to write8,397 as the product of9 and another factor. We can do this by dividing8,397 by9.
$Factor =8,397 /9$

Calculate the factor.
$Factor =8,397 /9 =933$ So,8,397 can be written as the product of9 and933.