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


33
34
35
36


Answer

 Option

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

 Option

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

 Option

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

 Option

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

 Option

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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