25.Разложите числа на простые множители. Для того, чтобы определить какой-либо делитель числа, используйте признаки делимости. A) 252 Б) 2520 B) 504 Г) 24800 Д) 936000 E)234000 Ж)51840 3)234 и) 1025000000

Разложение чисел на простые множители:

A) 252

1. $$252 : 2 = 126$$
2. $$126 : 2 = 63$$
3. $$63 : 3 = 21$$
4. $$21 : 3 = 7$$
5. $$7 : 7 = 1$$

\( 252 = 2^2 \cdot 3^2 \cdot 7 \)

Б) 2520

1. $$2520 : 2 = 1260$$
2. $$1260 : 2 = 630$$
3. $$630 : 2 = 315$$
4. $$315 : 3 = 105$$
5. $$105 : 3 = 35$$
6. $$35 : 5 = 7$$
7. $$7 : 7 = 1$$

\( 2520 = 2^3 \cdot 3^2 \cdot 5 \cdot 7 \)

B) 504

1. $$504 : 2 = 252$$
2. $$252 : 2 = 126$$
3. $$126 : 2 = 63$$
4. $$63 : 3 = 21$$
5. $$21 : 3 = 7$$
6. $$7 : 7 = 1$$

\( 504 = 2^3 \cdot 3^2 \cdot 7 \)

Г) 24800

1. $$24800 : 2 = 12400$$
2. $$12400 : 2 = 6200$$
3. $$6200 : 2 = 3100$$
4. $$3100 : 2 = 1550$$
5. $$1550 : 2 = 775$$
6. $$775 : 5 = 155$$
7. $$155 : 5 = 31$$
8. $$31 : 31 = 1$$

\( 24800 = 2^5 \cdot 5^2 \cdot 31 \)

Д) 936000

1. $$936000 : 2 = 468000$$
2. $$468000 : 2 = 234000$$
3. $$234000 : 2 = 117000$$
4. $$117000 : 2 = 58500$$
5. $$58500 : 2 = 29250$$
6. $$29250 : 2 = 14625$$
7. $$14625 : 3 = 4875$$
8. $$4875 : 3 = 1625$$
9. $$1625 : 5 = 325$$
10. $$325 : 5 = 65$$
11. $$65 : 5 = 13$$
12. $$13 : 13 = 1$$

\( 936000 = 2^6 \cdot 3^2 \cdot 5^3 \cdot 13 \)

E) 234000

1. $$234000 : 2 = 117000$$
2. $$117000 : 2 = 58500$$
3. $$58500 : 2 = 29250$$
4. $$29250 : 2 = 14625$$
5. $$14625 : 3 = 4875$$
6. $$4875 : 3 = 1625$$
7. $$1625 : 5 = 325$$
8. $$325 : 5 = 65$$
9. $$65 : 5 = 13$$
10. $$13 : 13 = 1$$

\( 234000 = 2^4 \cdot 3^2 \cdot 5^3 \cdot 13 \)

Ж) 51840

1. $$51840 : 2 = 25920$$
2. $$25920 : 2 = 12960$$
3. $$12960 : 2 = 6480$$
4. $$6480 : 2 = 3240$$
5. $$3240 : 2 = 1620$$
6. $$1620 : 2 = 810$$
7. $$810 : 2 = 405$$
8. $$405 : 3 = 135$$
9. $$135 : 3 = 45$$
10. $$45 : 3 = 15$$
11. $$15 : 3 = 5$$
12. $$5 : 5 = 1$$

\( 51840 = 2^7 \cdot 3^4 \cdot 5 \)

3) 234

1. $$234 : 2 = 117$$
2. $$117 : 3 = 39$$
3. $$39 : 3 = 13$$
4. $$13 : 13 = 1$$

\( 234 = 2 \cdot 3^2 \cdot 13 \)

и) 1025000000

1. $$1025000000 : 2 = 512500000$$
2. $$512500000 : 2 = 256250000$$
3. $$256250000 : 2 = 128125000$$
4. $$128125000 : 2 = 64062500$$
5. $$64062500 : 2 = 32031250$$
6. $$32031250 : 2 = 16015625$$
7. $$16015625 : 5 = 3203125$$
8. $$3203125 : 5 = 640625$$
9. $$640625 : 5 = 128125$$
10. $$128125 : 5 = 25625$$
11. $$25625 : 5 = 5125$$
12. $$5125 : 5 = 1025$$
13. $$1025 : 5 = 205$$
14. $$205 : 5 = 41$$
15. $$41 : 41 = 1$$

\( 1025000000 = 2^6 \cdot 5^{10} \cdot 41 \)