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# Find HCF and LCM of 404 and 96 and verify that HCF$×$LCM $ =$ Product of the two given numbers.

**Given:**Number 404 and 96.

**To do:**To Find HCF and LCM of 404 and 96 and verify that HCF$\times$LCM $=$ Product of the two given numbers.

**Solution:**

Using the factor tree for the prime factorization of

404 and 96, we have,

$404=2^{2}\times101$ and $96=2^{2}\times6$

To find the HCF, we list common prime factors and their smallest exponent in 404 and 96

As under :

Common prime factor $=2$, Least exponent$=2$

$\therefore$ HCF$=2^{2}=4$

To find the LCM,

we list all prime factors of 404 and 96 and their greatest exponent as follows:

Prime Factor of 404 and 96 | Greatest Exponent |

2 | 5 |

3 | 1 |

101 | 1 |

$\therefore$ LCM$=2^{5}\times3^{1}\times101^{1}=9696$

HCF$\times$ LCM $= 9696\times4 = 38784$

Product of two numbers $= 404\times96 = 38784$

Therefore HCF $\times$ LCM $=$ Product of two numbers.

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