Question
Easy
\begin{aligned} \text{If } x &= 2^3 \times 3^2 \times 5^3 \times 7^3 \\ y &= 2^2 \times 3^3 \times 5^4 \times 7^3 \text{, and } \\ z &= 2^4 \times 3^4 \times 5^2 \times 7^5 \text{, } \end{aligned} then H.C.F. of x, y and z is
1
$(30)^2 \times 7^3$
2
$(15)^3 \times 7^4$
3
$(30)^3 \times 7^3$
4
$30 \times 7^5$
Question Details
Time to Solve: 12
Exam: CTET
Level/Paper: CTET_P2
Chapter: Number Operations
Topic: LCM & HCF
Correct Answer
Option A
Explanation
To determine the H.C.F. (Highest Common Factor) of the numbers \(x\), \(y\), and \(z\), we need to find the smallest power of each prime factor that appears in all three numbers. Given: \[ x = 2^3 \times 3^2 \times 5^3 \times 7^3 \] \[ y = 2^2 \times 3^3 \times 5^4 \times 7^3 \] \[ z = 2^4 \times 3^4 \times 5^2 \times 7^5 \] Step-by-step Explanation: 1. **Prime Factor…Read More
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