: , ,
- , .
- , .
- 2 , 2.
- 5 , 0, 5.
- 10 , 0.
- , , 4 , 4 , .
- 3 , 3.
- 9 , 9.
. .
, 12=2 2 3. , 12 .
: 270
: | 270=2 3 3 3 5=2 33 5 |
. n , p , p2 n
48 60. 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. : 1, 2, 3, 4, 6, 12. 48 60, 12 .
. , . 48 : 48=24 3. 48: 4+1 1+1 =5 2=10. .. 2 1 3 1.
a b . HOD(a,b) : " HOD a b ". , HOD(a,b) = HOD(48,60) = 12.
. a b , HOD(a,b) = 1, .
: 26 35 , . 26=2 13 35=5 7, HOD(26,35) = 1.
, , , , , .
: HOD(56,84,96)
:
56=2 2 2 7=23 7
96=2 2 2 2 2 3=25 3
84=2 2 3 7=22 3 7
HOD(56,84,96) = 22 = 4
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14 16. , 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120. , 16: 16, 32, 48, 64, 80, 96, 112, 128. : 48 96. 14 12, 48 14 12.
a b . HOK(a,b) : " HOK a b ". , HOK(a,b) = HOK(14,12) = 48.
. a b HOK(a,b).
, , , , , .
: HOK(56,84,96)
: 56=2 2 2 7=23 7
96=2 2 2 2 2 3=25 7
84=2 2 3 7=22 3 7
HOK(56,84,96) = 25 3 7 = 672
. a b HOD(a b) HOK(a b)=ab. a b , .. HOD (a,b) = 1, HOK (a,b) = ab.
.
: , , , , , , , ,
: ba a: b, b , b =0,
- a . b
- a < b, ba
- a > b, ba . . : 67=161, 518=353
: ba cd a d=b c.
(ba cd):
- ba=b ka k - ,
- b = d, ba cd=ba c
- b =d, : ba cd=bdad cb. (b, d)
- k , k ba=bk a ba:k=ab k
- ba cd=a cb d ba:cd=b ca d
:
a + b = b + a -
(a + b) +c = a + (b + c) -
a + 0 = a -
a + (-a) = 0 -
:
a - (b + c) = a - b - c
(a + b) - c = (a - c) + b = a + (b - c) -
a - 0 = a -
0 - a = -a -
:
a b = b a -
(a b) c = a (b c) -
(a - b) c = a c - b c -
(a + b) c = a c + b c -
a 1 = a -
a 0 = 0 -
a a1=1 a =0 -
:
(a b): c = a (b: c) = (a: c) b -
(a + b): c = a: c + b: c -
(a - b): c = a: c - b: c -
a: (b c) = (a: b):c = (a: c): b -
a: 1 = a; 0: a = 0; a: a = 1, a =0-
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.
: ,
, .. 1% = 0,01
1% = 0,01, 2% = 0,02, 45% = 0,45, 350% = 3,5. : 5% = 0,05 = 120, 10% = 0,1 = 110, 20% = 0,2 = 51, 25% = 0,25 = 41, 50% = 0,5 = 21, 75% = 0,75 =43
.
- ? : x= 100%
- 20%, 25%. , , ? : 1) 1= (100% + 20%) = 120% = 1,2 2) 2= (100% - 25%)1 = 75%1 = 0,751 = 0,75 1,2 = 0,9 = 90% 3) 2 - = 90% - 100% = -10%. : 10%.
- , 25%? : 1) t=SV 2) t1=SV1=S1 25V=11 25SV=0 8SV=80%t. : 20%.