1.  Find the H.C.F of 108, 288 and 360

33
34
35
36

```Answer

Answer: Option  D Explanation:108 = 2^2 * 3^3,
288 = 2^5 * 3^2
360 = 2^3 *5 * 3^2
H.C.F = 2^2 * 3^2 = 36 ```

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2.  The H.C.F of 204, 1190 and 1445 is?

17
18
19
21

```Answer

Answer: Option  A Explanation:204 = 2^2*3*17;  1190 = 2*5*7*17; 1445 = 5*17^2.
Therefore H.C.F. = 17. ```

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3.  H.C.F. of 3240, 3600 and a third number is 36 and their L.C.M. is 2^4*3^5*5^2*7^2 the third number is?

2^2*3^5*7^2
2^2*5^3*7^2
2^5*5^2*7^2
2^3*3^5*7^2

```Answer

Answer: Option  A Explanation:3240 = 2^3*3^4*5;  3600 = 2^4*3^2*5^2;  H.C.F. = 36 =2^2*3^2.
Since H.C.F. is the product of lowest powers of common factors, so the third number must have (2^2*3^2) as its factor.
Since L.C.M. is the product of highest powers of common prime factors, so the third number must have 3^5 and 7^2 as its factors.
Therefore third number = 2^2*3^5*7^2. ```

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4.  Find the highest common factor of 36 and 84?

4
6
12
18

```Answer

Answer: Option  C Explanation:36 = 2^2*3^2; 84 = 2^2*3*7.
Therefore H.C.F = 2^2*3 =12 ```

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5.  H.C.F of 4*27* 3125, 8*9*25*7 & 16*81*5*11*49 is?

180
360
540
1260

```Answer

Answer: Option  A Explanation:4*27*3125 = 2^2*3^3*5^5;  8*9*25*7 = 2^3*3^2*5^2*7;
16*81*5*11*49 = 2^4*3^4*5*7^2*11
Therefore H.C.F = 2^2*3^2*5 = 180. ```

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