Question 14 of 18beginner🔧 ApplyMCQ1 mark

Among the numbers below, which is the largest number that perfectly divides both 306 and 36? (a) 36 (b) 612 (c) 18 (d) 3 (e) 2 (f) 360

Exercise: Figure it Out (Section 6) | Q: 16 | (Page Page 18)
For More Understanding

Explanation

The largest number that perfectly divides both 306 and 36 is their HCF. Finding HCF: 306 = 2×32 \times 3² × 17 and 36 = 2² × 3². Common factors: 2 and 3². HCF = 2×92 \times 9 = 18. From the options, 18 is the largest common factor. Note that 36 does not divide 306 (306 ÷ 36 = 8.5), 612 and 360 are larger than both numbers so cannot be factors.

Solution Steps

  1. Step 1: Find prime factorisation: 306 = 2×32 \times 3² × 17, 36 = 2² × 3².

  2. Step 2: Find HCF = 2×32 \times 3² = 18.

  3. Step 3: Check options: 36 doesn't divide 306, 612 > 306, 18 works, 3 and 2 are smaller.

  4. Step 4: The largest valid option is 18.

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