They are not interchangeable. 번호 is used to mark items or list things. ex) 1번 후보 candidate number one ex) 1번 문 Gate 1 ex) 101번 방 Room 101 숫자 is a general term for a number. 숫자 can be big or small, and can be calculated. Similar to a figure. ex) 숫자가 크다/작다 The number is big/small. ex) 여러 숫자들이 많다 There are many different numbers. ex) 숫자 계산 calculation of numbers 수치 is a resulting number after measurement or calculation. ex) 혈압수치 blood pressure

Literally, The word 숫자(數字) -- 수(數)의 자(字) -- refers to a digit, one of the written signs that present the numbers, and it is often used to show an amount or quantity. The word 번호(番號) refers to a number used to show the position of something in an ordered set or list. So, when talking about a phone number, we say "전화 번호", not "전화 숫자". When counting the number, we should say that"숫자를 세다", not that "번호를 세다".

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