Question

find the greatest number which can divide 83, 53 and 77 leaving a remainder 5 in each case​

Answer 1

Answer: 12

Step-by-step explanation:

Find the numbers without the remainder 5:

89 - 5 = 84

53 - 5 = 48

77 - 5 = 72

Find the Highest Common Factor:

84 = 2² × 3 × 7

48 = 2⁴ × 3

72 = 2³ × 3²

HCF = 2² × 3

HCF = 12

Answer 2

Answer:

STEP 1 : SUBTRACT THE REMINDER FROM GIVEN NUMBERS

83-5 = 78

77-5 = 72

53-5 = 48

STEP 2 : EXPAND THE NUMBERS

78 = 2×3×13

72 = 2×2×2×3×3

48 = 2×2×2×2×3

STEP 3 : FIND THE GREATEST COMMON NUMBER BETWEEN THEM.

THE GREATEST NUMBER WHICH WHOULD LEAVE THE REMINDER OF '5' AFTER DIVIDING '83', '77', and '53' is "6" (2×3).