Which of the following numbers are divisible by 2, 4 or 8:

(i) 54014

(ii) 723840

(iii) 6531088

(iv) 75689604

(v) 786235

(vi) 5321048

A number is divisible by 2 if its last digit is 0, 2, 4, 6 or 8.

A number is divisible by 4 if the number formed by its last two digits is divisible by 4.

A number is divisible by 8 if the number formed by its last three digits is divisible by 8.

(i) 54014 — last digit 4, divisible by 2.

Last two digits = 14, not divisible by 4.

Hence, 54014 is divisible by 2 only.

(ii) 723840 — last digit 0, divisible by 2.

Last two digits = 40, divisible by 4.

Last three digits = 840, and 840 ÷ 8 = 105, divisible by 8.

Hence, 723840 is divisible by 2, 4 and 8.

(iii) 6531088 — last digit 8, divisible by 2.

Last two digits = 88, divisible by 4.

Last three digits = 088 = 88, and 88 ÷ 8 = 11, divisible by 8.

Hence, 6531088 is divisible by 2, 4 and 8.

(iv) 75689604 — last digit 4, divisible by 2.

Last two digits = 04 = 4, divisible by 4.

Last three digits = 604, and 604 is not divisible by 8 because 8 × 75 = 600 and remainder is 4.

Hence, 75689604 is divisible by 2 and 4 only.

(v) 786235 — last digit 5, not divisible by 2.

Hence, 786235 is not divisible by 2, 4 or 8.

(vi) 5321048 — last digit 8, divisible by 2.

Last two digits = 48, divisible by 4.

Last three digits = 048 = 48, and 48 ÷ 8 = 6, divisible by 8.

Hence, 5321048 is divisible by 2, 4 and 8.