If x = 3¹27} × 5¹21} × 7¹6} y = 3¹285¹19} × 7²1} z = 3¹26× 5¹20} × 7¹9}, {then} HCF of x, y and z is

Correct Answer is : 3126×5119×7163¹26} × 5¹19} × 7¹6}3126×5119×716

Correct Answer is : 3126×5119×7163¹26} × 5¹19} × 7¹6}3126×5119×716

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CTET Paper II (Mathematics and Science) 10 Jan 2022 Solved Paper

Question : 33 of 150

Marks: +1, -0

If x = 3^{127} × 5^{121} × 7^{16}

y = 3

5^{119} \times 7^{21}

z = 3

\times 5^{120} \times 7^{19}, \text{then}

HCF of x, y and z is

Solution:

Concept:

HCF is the product of the smallest powers of all common prime factors in the given numbers.

Explanation:

For prime 3: exponents are 127, 128, 126. The smallest is 126.

For prime 5: exponents are 121, 119, 120. The smallest is 119.

For prime 7: exponents are 16, 21, 19. The smallest is 16.

Thus, HCF =

3^{126} \times 5^{119} \times 7^{16}

Answer:

3^{126} \times 5^{119} \times 7^{16}

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