Math / Numbers & Operations

Question5. If 21 divides $m$ , what else must divide $m$ ?

Studdy Solution

STEP 1

1. The integer $m$ is divisible by $21$ .
2. We need to determine other divisors of $m$ based on its divisibility by $21$ .

STEP 2

1. Factorize 21.
2. Identify divisors of 21.
3. Conclude divisors of $m$ .

STEP 3

Factorize $21$ into its prime factors.
$21 = 3 \times 7$

STEP 4

Identify all divisors of $21$ using its prime factorization.
The divisors of $21$ are $1, 3, 7,$ and $21$ .

STEP 5

Conclude that if $21$ divides $m$ , then all divisors of $21$ must also divide $m$ .
Therefore, $m$ must be divisible by $1, 3, 7,$ and $21$ .
The divisors of $m$ must include:
$\boxed{1, 3, 7, \text{ and } 21}$

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Question5. If 21 divides $m$ , what else must divide $m$ ?

Studdy Solution

STEP 1

1. The integer $m$ is divisible by $21$ .
2. We need to determine other divisors of $m$ based on its divisibility by $21$ .

STEP 2

1. Factorize 21.
2. Identify divisors of 21.
3. Conclude divisors of $m$ .

STEP 3

Factorize $21$ into its prime factors.
$21 = 3 \times 7$

STEP 4

Identify all divisors of $21$ using its prime factorization.
The divisors of $21$ are $1, 3, 7,$ and $21$ .

STEP 5

Conclude that if $21$ divides $m$ , then all divisors of $21$ must also divide $m$ .
Therefore, $m$ must be divisible by $1, 3, 7,$ and $21$ .
The divisors of $m$ must include:
$\boxed{1, 3, 7, \text{ and } 21}$

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Question5. If 21 divides mmm, what else must divide mmm ?

Studdy Solution

STEP 1

1. The integer m m m is divisible by 21 21 21.2. We need to determine other divisors of m m m based on its divisibility by 21 21 21.

STEP 2

1. Factorize 21.2. Identify divisors of 21.3. Conclude divisors of m m m.

STEP 3

Factorize 21 21 21 into its prime factors.21=3×7 21 = 3 \times 7 21=3×7

STEP 4

Identify all divisors of 21 21 21 using its prime factorization.The divisors of 21 21 21 are 1,3,7, 1, 3, 7, 1,3,7, and 21 21 21.

STEP 5

Conclude that if 21 21 21 divides m m m, then all divisors of 21 21 21 must also divide m m m.Therefore, m m m must be divisible by 1,3,7, 1, 3, 7, 1,3,7, and 21 21 21. The divisors of m m m must include:1,3,7, and 21\boxed{1, 3, 7, \text{ and } 21}1,3,7, and 21​

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Question5. If 21 divides $m$ , what else must divide $m$ ?

1. The integer $m$ is divisible by $21$ .
2. We need to determine other divisors of $m$ based on its divisibility by $21$ .

1. Factorize 21.
2. Identify divisors of 21.
3. Conclude divisors of $m$ .

Factorize $21$ into its prime factors.
$21 = 3 \times 7$

Identify all divisors of $21$ using its prime factorization.
The divisors of $21$ are $1, 3, 7,$ and $21$ .

Conclude that if $21$ divides $m$ , then all divisors of $21$ must also divide $m$ .
Therefore, $m$ must be divisible by $1, 3, 7,$ and $21$ .
The divisors of $m$ must include:
$\boxed{1, 3, 7, \text{ and } 21}$