How many 3 digit numbers give a remainder of 4 when divided by 7.

1.	How many 3 digit numbers give a remainder of 4 when divided by 7.
Answer» Smallest 3 digit number which leaves remainder 4 when divided 7 is 102. Largest 3 digit number which leaves remainder 4 when divided by 7 is 998. 102, 109, ....... 998 is A.P. of such numbers. \(\therefore 998 = 102 + (n -1)7\) ⇒ \(n - 1 = \frac{998 - 102}{7} = \frac{896}{7} = 128\) ⇒ \(n = 129\) Hence, total 129, 3 digit numbers give a remainder 4 when divided by 7.

Answer»

Smallest 3 digit number which leaves remainder 4 when divided 7 is 102.

Largest 3 digit number which leaves remainder 4 when divided by 7 is 998.

102, 109, ....... 998 is A.P. of such numbers.

\(\therefore 998 = 102 + (n -1)7\)

⇒ \(n - 1 = \frac{998 - 102}{7} = \frac{896}{7} = 128\)

⇒ \(n = 129\)

Hence, total 129, 3 digit numbers give a remainder 4 when divided by 7.

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How many 3 digit numbers give a remainder of 4 when divided by 7.

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