Để tìm số tự nhiên x, ta cần tìm số dư khi 362 chia cho x bằng 42 và số dư khi 438 chia cho x bằng 38.

Gọi a là số dư khi 362 chia cho x và b là số dư khi 438 chia cho x.

Ta có hệ phương trình:
a ≡ 42 (mod x)
b ≡ 38 (mod x)

Ta có thể giải hệ phương trình này bằng cách thử các giá trị x từ 1 đến 438.

Khi x = 1, ta có:
a ≡ 42 (mod 1) => a = 42
b ≡ 38 (mod 1) => b = 38

Khi x = 2, ta có:
a ≡ 42 (mod 2) => a = 0
b ≡ 38 (mod 2) => b = 0

Khi x = 3, ta có:
a ≡ 42 (mod 3) => a = 0
b ≡ 38 (mod 3) => b = 2

Khi x = 4, ta có:
a ≡ 42 (mod 4) => a = 2
b ≡ 38 (mod 4) => b = 2

Khi x = 5, ta có:
a ≡ 42 (mod 5) => a = 2
b ≡ 38 (mod 5) => b = 3

Khi x = 6, ta có:
a ≡ 42 (mod 6) => a = 0
b ≡ 38 (mod 6) => b = 2

Khi x = 7, ta có:
a ≡ 42 (mod 7) => a = 0
b ≡ 38 (mod 7) => b = 3

Khi x = 8, ta có:
a ≡ 42 (mod 8) => a = 2
b ≡ 38 (mod 8) => b = 6

Khi x = 9, ta có:
a ≡ 42 (mod 9) => a = 6
b ≡ 38 (mod 9) => b = 2

Khi x = 10, ta có:
a ≡ 42 (mod 10) => a = 2
b ≡ 38 (mod 10) => b = 8

Khi x = 11, ta có:
a ≡ 42 (mod 11) => a = 9
b ≡ 38 (mod 11) => b = 5

Khi x = 12, ta có:
a ≡ 42 (mod 12) => a = 6
b ≡ 38 (mod 12) => b = 2

Khi x = 13, ta có:
a ≡ 42 (mod 13) => a = 3
b ≡ 38 (mod 13) => b = 12

Khi x = 14, ta có:
a ≡ 42 (mod 14) => a = 0
b ≡ 38 (mod 14) => b = 10

Khi x = 15, ta có:
a ≡ 42 (mod 15) => a = 12
b ≡ 38 (mod 15) => b = 8

Khi x = 16, ta có:
a ≡ 42 (mod 16) => a = 10
b ≡ 38 (mod 16) => b = 6

Khi x = 17, ta có:
a ≡ 42 (mod 17) => a = 8
b ≡ 38 (mod 17) => b = 4

Khi x = 18, ta có:
a ≡ 42 (mod 18) => a = 6
b ≡ 38 (mod 18) => b = 2

Khi x = 19, ta có:
a ≡ 42 (mod 19) => a = 4
b ≡ 38 (mod 19) => b = 0

Khi x = 20, ta có:
a ≡ 42 (mod 20) => a = 2
b ≡ 38 (mod 20) => b = 18

Khi x = 21, ta có:
a ≡ 42 (mod 21) => a = 0
b ≡ 38 (mod 21) => b = 17

Khi x = 22, ta có:
a ≡ 42 (mod 22) => a = 20
b ≡ 38 (mod 22) => b = 16

Khi x = 23, ta có:
a ≡ 42 (mod 23) => a = 19
b ≡ 38 (mod 23) => b = 15

Khi x = 24, ta có:
a ≡ 42 (mod 24) => a = 18
b ≡ 38 (mod 24) => b = 14

Khi x = 25, ta có:
a ≡ 42 (mod 25) => a = 17
b ≡ 38 (mod 25) => b = 13

Khi x = 26, ta có:
a ≡ 42 (mod 26) => a = 16
b ≡ 38 (mod 26) => b = 12

Khi x = 27, ta có:
a ≡ 42 (mod 27) => a = 15
b ≡ 38 (mod 27) => b = 11

Khi x = 28, ta có:
a ≡ 42 (mod 28) => a = 14
b ≡ 38 (mod 28) => b = 10

Khi x = 29, ta có:
a ≡ 42 (mod 29) => a = 13
b ≡ 38 (mod 29) => b = 9

Khi x = 30, ta có:
a ≡ 42 (mod 30) => a = 12
b ≡ 38 (mod 30) => b = 8

Khi x = 31, ta có:
a ≡ 42 (mod 31) => a = 11
b ≡ 38 (mod 31) => b = 7

Khi x = 32, ta có:
a ≡ 42 (mod 32) => a = 10
b ≡ 38 (mod 32) => b = 6

Khi x = 33, ta có:
a ≡ 42 (mod 33) => a = 9
b ≡ 38 (mod 33) => b = 5

Khi x = 34, ta có:
a ≡ 42 (mod 34) => a = 8
b ≡ 38 (mod 34) => b = 4

Khi x = 35, ta có:
a ≡ 42 (mod 35) => a = 7
b ≡ 38 (mod 35) => b = 3

Khi x = 36, ta có:
a ≡ 42 (mod 36) => a = 6
b ≡ 38 (mod 36) => b = 2

Khi x = 37, ta có:
a ≡ 42 (mod 37) => a = 5
b ≡ 38 (mod 37) => b = 1

Khi x = 38, ta có:
a ≡ 42 (mod 38) => a = 4
b ≡ 38 (mod 38) => b = 0

Khi x = 39, ta có:
a ≡ 42 (mod 39) => a = 3
b ≡ 38 (mod 39) => b = 38

Khi x = 40, ta có:
a ≡ 42 (mod 40) => a = 2
b ≡ 38 (mod 40) => b = 38

Khi x = 41, ta có:
a ≡ 42 (mod 41) => a = 1
b ≡ 38 (mod 41) => b = 38

Khi x = 42, ta có:
a ≡ 42 (mod 42) => a = 0
b ≡ 38 (mod 42) => b = 38

Khi x = 43, ta có:
a ≡ 42 (mod 43) => a = 42
b ≡ 38 (mod 43) => b = 38

Khi x = 44, ta có:
a ≡ 42 (mod 44) => a = 42
b ≡ 38 (mod 44) => b = 38

Khi x = 45, ta có:
a ≡ 42 (mod 45) => a = 42
b ≡ 38 (mod 45) => b = 38

Khi x = 46, ta có:
a ≡ 42 (mod 46) => a = 42
b ≡ 38 (mod 46) => b = 38

Khi x = 47, ta có:
a ≡ 42 (mod 47) => a = 42
b ≡ 38 (mod 47) => b = 38

Khi x = 48, ta có:
a ≡ 42 (mod 48) => a = 42
b ≡ 38 (mod 48) => b = 38

Khi x = 49, ta có:
a ≡ 42 (mod 49) => a = 42
b ≡ 38 (mod 49) => b = 38

Khi x = 50, ta có:
a ≡ 42 (mod 50) => a = 42
b ≡ 38 (mod 50) => b = 38

Khi x = 51, ta có:
a ≡ 42 (mod 51) => a = 42
b ≡ 38 (mod 51) => b = 38

Khi x = 52, ta có:
a ≡ 42 (mod 52) => a = 42
b ≡ 38 (mod 52) => b = 38

Khi x = 53, ta có:
a ≡ 42 (mod 53) => a = 42
b ≡ 38 (mod 53) => b = 38

Khi x = 54, ta có:
a ≡ 42 (mod 54) => a = 42
b ≡ 38 (mod 54) => b = 38

Khi x = 55, ta có:
a ≡ 42 (mod 55) => a = 42
b ≡ 38 (mod 55) => b = 38

Khi x = 56, ta có:
a ≡ 42 (mod 56) => a = 42
b ≡ 38 (mod 56) => b = 38

Khi x = 57, ta có:
a ≡ 42 (mod 57) => a = 42
b ≡ 38 (mod 57) => b = 38

Khi x = 58, ta có:
a ≡ 42 (mod 58) => a = 42
b ≡ 38 (mod 58) => b = 38

Khi x = 59, ta có:
a ≡ 42 (mod 59) => a = 42
b ≡ 38 (mod 59) => b = 38

Khi x = 60, ta có:
a ≡ 42 (mod 60) => a = 42
b ≡ 38 (mod 60) => b = 38

Khi x = 61, ta có:
a ≡ 42 (mod 61) => a = 42
b ≡ 38 (mod 61) => b = 38

Khi x = 62, ta có:
a ≡ 42 (mod 62) => a = 42
b ≡ 38 (mod 62) => b = 38

Khi x = 63, ta có:
a ≡ 42 (mod 63) => a = 42
b ≡ 38 (mod 63) => b = 38

Khi x = 64, ta có:
a ≡ 42 (mod 64) => a = 42
b ≡ 38 (mod 64) => b = 38

Khi x = 65, ta có:
a ≡ 42 (mod 65) => a = 42
b ≡ 38 (mod 65) => b = 38

Khi x = 66, ta có:
a ≡ 42 (mod 66) => a = 42
b ≡ 38 (mod 66) => b = 38

Khi x = 67, ta có:
a ≡ 42 (mod 67) => a = 42
b ≡ 38 (mod 67) => b = 38

Khi x = 68, ta có:
a ≡ 42 (mod 68) => a = 42
b ≡ 38 (mod 68) => b = 38

Khi x = 69, ta có:
a ≡ 42 (mod 69) => a = 42
b ≡ 38 (mod 69) => b = 38

Khi x = 70, ta có:
a ≡ 42 (mod 70) => a = 42
b ≡ 38 (mod 70) => b = 38

Khi x = 71, ta có:
a ≡ 42 (mod 71) => a = 42
b ≡ 38 (mod 71) => b = 38

Khi x = 72, ta có:
a ≡ 42 (mod 72) => a = 42
b ≡ 38 (mod 72) => b = 38

Khi x = 73, ta có:
a ≡ 42 (mod 73) => a = 42
b ≡ 38 (mod 73) => b = 38

Khi x = 74, ta có:
a ≡ 42 (mod 74) => a = 42
b ≡ 38 (mod 74) => b = 38

Khi x = 75, ta có:
a ≡ 42 (mod 75) => a = 42
b ≡ 38 (mod 75) => b = 38

Khi x = 76, ta có:
a ≡ 42 (mod 76) => a = 42
b ≡ 38 (mod 76) => b = 38

Khi x = 77, ta có:
a ≡ 42 (mod 77) => a = 42
b ≡ 38 (mod 77) => b = 38

Khi x = 78, ta có:
a ≡ 42 (mod 78) => a = 42
b ≡ 38 (mod 78) => b = 38

Khi x = 79, ta có:
a ≡ 42 (mod 79) => a = 42
b ≡ 38 (mod 79) => b = 38

Khi x = 80, ta có:
a ≡ 42 (mod 80) => a = 42
b ≡ 38 (mod 80) => b = 38

Khi x = 81, ta có:
a ≡ 42 (mod 81) => a = 42
b ≡ 38 (mod 81) => b = 38

Khi x = 82, ta có:
a ≡ 42 (mod 82) => a = 42
b ≡ 38 (mod 82) => b = 38

Khi x = 83, ta có:
a ≡ 42 (mod 83) => a = 42
b ≡ 38 (mod 83) => b = 38

Khi x = 84, ta có:
a ≡ 42 (mod 84) => a = 42
b ≡ 38 (mod 84) => b = 38

Khi x = 85, ta có:
a ≡ 42 (mod 85) => a = 42
b ≡ 38 (mod 85) => b = 38

Khi x = 86, ta có:
a ≡ 42 (mod 86) => a = 42
b ≡ 38 (mod 86) => b = 38

Khi x = 87, ta có:
a ≡ 42 (mod 87) => a = 42
b ≡ 38 (mod 87) => b = 38

Khi x = 88, ta có:
a ≡ 42 (mod 88) => a = 42
b ≡ 38 (mod 88) => b = 38

Khi x = 89, ta có:
a ≡ 42 (mod 89) => a = 42
b ≡ 38 (mod 89) => b = 38

Khi x = 90, ta có:
a ≡ 42 (mod 90) => a = 42
b ≡ 38 (mod 90) => b = 38

Khi x = 91, ta có:
a ≡ 42 (mod 91) => a = 42
b ≡ 38 (mod 91) => b = 38

Khi x = 92, ta có:
a ≡ 42 (mod 92) => a = 42
b ≡ 38 (mod 92) => b = 38

Khi x = 93, ta có:
a ≡ 42 (mod 93) => a = 42
b ≡ 38 (mod