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Number - Prime Factorisation
a - answer s - solution v - video d - discussion
Are the following numbers prime numbers?
a) $4$ a
Question ID: 10190010010
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Question by: ada
Answer by: ada
Prime numbers can only be divided by $1$ and itself. $4$ can be divided by $1$, $2$ and $4$ so is not a prime number.
Solution by: ada
Video by:
b) $5$ a
Prime numbers can only be divided by $1$ and itself. $5$ can be divided by $1$ and $5$ only so is a prime number.
c) $6$ a
Prime numbers can only be divided by $1$ and itself. $6$ can be divided by $1$, $2$, $3$ and $6$ so is not a prime number.
d) $7$ a
e) $8$ a
Prime numbers can only be divided by $1$ and itself. $8$ can be divided by $1$, $2$ and $4$ and $8$ so is not a prime number.
f) $9$ a
g) $10$ a
Prime numbers can only be divided by $1$ and itself. $10$ can be divided by $1$, $2$, $5$ and $10$ so is not a prime number.
h) $11$ a
Prime numbers can only be divided by $1$ and itself. $11$ can be divided by $1$ and $11$ only so is a prime number.
It is tricky to explain why $1$ is not a prime number. Prime numbers can only be divided by $1$ and itself. $1$ is divisible by $1$ only which is itself. Therefore it is not prime.
b) $17$ a
Solution by:
c) $27$ a
d) $29$ a
e) $47$ a
f) $51$ a
h) $129$ a
Express the following as a product of their prime factors
$2\times3$
$2\times13$
a) $30$ a
$2\times3\times5$
c) $105$ a
d) $110$ a
$2\times5\times11$
f) $231$ a
$2^2\times3$
$2\times3^2$
a) $7\times11$ a
$77$
b) $2^2\times5$ a
c) $5^2\times11$ a
$275$
d) $3\times5\times13$ a
e) $3^2\times13$ a
f) $2\times13\times29$ a
$2^2\times3^2$
$2\times3^2\times5$
$3^2\times5\times7$
e) $600$ a
$2^3\times3\times5^2$
f) $2352$ a
Which number is represented by the following prime factorisations?
$7$
$2^2$
a) $300$ a
b) $14\,850$ a
$2\times3^3\times5^2\times11$
c) $14\,300$ a
$2^2\times5^2\times11\times13$
d) $3267$ a
$3^3\times11^2$
e) $30\,030$ a
$2\times3\times5\times7\times11\times13$
f) $33\,813$ a
$3^2\times13\times17^2$
It is known that $12=2^2\times3$. Use this to find the prime factorisation of:
$2^3\times3^2\times5$
It is known that $30=2\times3\times5$. Use this to find the prime factorisation of:
$2\times3\times5\times7$
$2\times3\times5^2$
$2^2\times3^2\times5^2$
It is known that $360=2^3\times3^2\times5$. Use this to find the prime factorisation of:
b) $3600$ a
By using prime factorisation, list all the positive factors for:
$1,2,3,5,6,10,15,30$
$1, 2, 3, 4, 6, 12$
$1, 2, 3, 6, 9, 18, 27, 54$
$1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90$
$1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140$
g) $312$ a
$1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312$
$1, 2, 5, 10, 13, 25, 26, 50, 65, 130, 325, 650$
By using prime factorisation, find the square root of the following:
f) $129600$ a
By using prime factorisation, find...
a) The cube root of $125$ a
b) The cube root of $216$ a
c) The cube root of $512$ a
d) The fourth root of $1296$ a
e) The fourth root of $160000$ a
f) The fifth root of $248832$ a
What is the lowest multiplier needed in order to make the following square numbers:
f) $22869$ a
What is the lowest multiplier needed in order to make the following cube numbers:
a) $4$
b) $5$
c) $6$
d) $7$
e) $8$
f) $9$
g) $10$
h) $11$
b) $17$
c) $27$
d) $29$
e) $47$
f) $51$
h) $129$
a) $30$
c) $105$
d) $110$
f) $231$
a) $7\times11$
b) $2^2\times5$
c) $5^2\times11$
d) $3\times5\times13$
e) $3^2\times13$
f) $2\times13\times29$
e) $600$
f) $2352$
a) $300$
b) $14\,850$
c) $14\,300$
d) $3267$
e) $30\,030$
f) $33\,813$
b) $3600$
g) $312$
f) $129600$
a) The cube root of $125$
b) The cube root of $216$
c) The cube root of $512$
d) The fourth root of $1296$
e) The fourth root of $160000$
f) The fifth root of $248832$
f) $22869$
a) No
b) Yes
c) No
d) Yes
e) No
f) No
g) No
h) Yes
e) Yes
g) Yes
h) No
a) $2\times3$
b) $2\times5$
c) $2\times7$
d) $2\times13$
e) $3\times11$
f) $5\times7$
a) $2\times3\times5$
b) $2\times5\times7$
c) $3\times5\times7$
e) $2\times3\times13$
f) $3\times7\times11$
a) $2^2\times3$
b) $2\times3^2$
c) $3^2\times7$
d) $2\times5^2$
e) $2^3\times3$
f) $3^3\times5$
a) $2^2\times3^2$
b) $2\times3^2\times5$
c) $2^2\times5^2$
d) $3^2\times5\times7$
e) $2^3\times3\times5^2$
f) $2^4\times3\times7^2$
c) $2^2$
d) $7^2$
f) $3^3$
a) $2^2\times3\times5^2$
b) $2\times3^3\times5^2\times11$
c) $2^2\times5^2\times11\times13$
d) $3^3\times11^2$
e) $2\times3\times5\times7\times11\times13$
f) $3^2\times13\times17^2$
a) $2^2\times3\times5$
b) $2^2\times3\times7$
d) $2^2\times3^2$
e) $2\times3$
f) $2^3\times3^2\times5$
a) $2\times3\times5\times7$
c) $2\times3\times5^2$
d) $2^2\times3\times5^2$
f) $2^2\times3^2\times5^2$
a) $2^4\times3^2\times5$
b) $2^4\times3^2\times5^2$
c) $2^2\times3^2\times5$
d) $2\times3\times5$
e) $2\times3\times5$
a) $1,2,3,5,6,10,15,30$
b) $1, 2, 3, 4, 6, 12$
c) $1, 2, 3, 6, 9, 18, 27, 54$
d) $1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90$
e) $1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140$
f) $1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160$
g) $1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312$
h) $1, 2, 5, 10, 13, 25, 26, 50, 65, 130, 325, 650$
a) Prime numbers can only be divided by $1$ and itself. $4$ can be divided by $1$, $2$ and $4$ so is not a prime number.
b) Prime numbers can only be divided by $1$ and itself. $5$ can be divided by $1$ and $5$ only so is a prime number.
c) Prime numbers can only be divided by $1$ and itself. $6$ can be divided by $1$, $2$, $3$ and $6$ so is not a prime number.
d) Prime numbers can only be divided by $1$ and itself. $7$ can be divided by $1$ and $7$ only so is a prime number.
e) Prime numbers can only be divided by $1$ and itself. $8$ can be divided by $1$, $2$ and $4$ and $8$ so is not a prime number.
f) Prime numbers can only be divided by $1$ and itself. $9$ can be divided by $1$, $3$ and $9$ so is not a prime number.
g) Prime numbers can only be divided by $1$ and itself. $10$ can be divided by $1$, $2$, $5$ and $10$ so is not a prime number.
h) Prime numbers can only be divided by $1$ and itself. $11$ can be divided by $1$ and $11$ only so is a prime number.
a) It is tricky to explain why $1$ is not a prime number. Prime numbers can only be divided by $1$ and itself. $1$ is divisible by $1$ only which is itself. Therefore it is not prime.
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