Q. 1
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
What is the highest common factor (HCF) of 16 and 36?
💡
Step-by-Step Explanation & Concept Rationale
Prime factorizations: \[16 = 2^4\] \[36 = 2^2 \times 3^2\] The common prime factor with the smallest exponent is $2^2 = 4$. Thus, the HCF is $4$. Thus, the correct option is (B).
Q. 2
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
What is the highest common factor (HCF) of 36 and 82?
💡
Step-by-Step Explanation & Concept Rationale
Prime factorizations: \[36 = 2^2 \times 3^2\] \[82 = 2 \times 41\] The common prime factor is $2^1 = 2$. Thus, the HCF is $2$. Thus, the correct option is (A).
Q. 3
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
What is the highest common factor (HCF) of 6 and 12?
💡
Step-by-Step Explanation & Concept Rationale
Since 6 divides 12 evenly ($12 \div 6 = 2$), the highest common factor is $6$. Thus, the correct option is (C).
Q. 4
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
What is the highest common factor (HCF) of 50, 70, and 85?
💡
Step-by-Step Explanation & Concept Rationale
Prime factorizations: \[50 = 2 \times 5^2\] \[70 = 2 \times 5 \times 7\] \[85 = 5 \times 17\] The only common prime factor is $5$. Therefore: \[\text{HCF} = 5\] Thus, the correct option is (A).
Q. 5
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
What is the highest common factor (HCF) of 17, 23, 27, and 29?
💡
Step-by-Step Explanation & Concept Rationale
The numbers 17, 23, and 29 are prime numbers. Since there is no common factor greater than 1 dividing all four numbers: \[\text{HCF}(17, 23, 27, 29) = 1\] Thus, the correct option is (A).
Q. 6
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
What is the highest common factor (HCF) of 10, 20, 25, and 35?
💡
Step-by-Step Explanation & Concept Rationale
Prime factorizations: \[10 = 2 \times 5\] \[20 = 2^2 \times 5\] \[25 = 5^2\] \[35 = 5 \times 7\] The common prime factor with the smallest exponent is $5^1 = 5$. Thus, the HCF is $5$. Thus, the correct option is (B).
Q. 7
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
What is the Highest Common Factor (HCF) of $10$ and $12$?
💡
Step-by-Step Explanation & Concept Rationale
Prime factorizations: $10 = 2 \times 5$ and $12 = 2^2 \times 3$. The only common prime factor is $2^1 = 2$. Therefore, $\text{HCF}(10, 12) = 2$. Thus, the correct option is (B).
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