**Question:** An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?

Class | 10th |

Subject | Maths |

Chapter | Real Numbers |

Exercise | 1.1 |

Previous Question | Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer. |

Next Question | Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m. |

**Solution:**

Given,

Number of army contingent members=616

Number of army band members = 32

If the two groups have to march in the same column, we have to find out the highest common factor between the two groups.

HCF(616, 32), gives the maximum number of columns in which they can march.

Using Euclid’s algorithm to find their HCF, we get,

Since, 616>32,

therefore,

616 = 32 × 19 + 8

Since, 8 ≠ 0, therefore, taking 32 as new divisor, we have,

32 = 8 × 4 + 0

Now we have got remainder as 0, therefore, HCF (616, 32) = 8.

Hence, the maximum number of columns in which they can march is 8.