6
Find the greatest number which divides 742 and 1162find the greatest number which divides 742 and 1162 117
To determine factors of a number it is necessary to divide the number by prime numbers of increasing value. If there is no remainder then the prime number is a factor. The square root of 231 is approximately 15 so it is necessary to divide by all the prime numbers up to 13 (15 is not a prime number). 231 ÷ 2 leaves a remainder of 1 231 ÷ 3 divides exactly 77 times (which is 7 x 11 - both are prime numbers) 231 ÷ 5 leaves a remainder of 1 231 ÷ 7 divides exactly 33 times (which is 3 x 11 - both are prime numbers) 231 ÷ 11 divides exactly 21 times (which is 3 x 7 - both are prime numbers) 231 ÷ 13 leaves a remainder of 10 If we multiply together the three numbers that are shown to be factors 3 x 7 x 11 = 231 this confirms that there are no other factors of 231 except 1 and 231 itself. This last condition is true for every positive integer. 231 is divisible by 1, 3, 7, 11 and 231
Let the greatest number be 'x'. Then nx + 7 = 742 : nx = 735 And mx + 7 = 1162 :mx = 1155 The number required is the Greatest Common Factor of 735 and 1155. 735 expressed as the product of its prime factors = 3 x 5 x 7 x 7 1155 expressed as the product of its prime factors = 3 x 5 x 7 x 11 The GCF is 3 x 5 x 7 = 105
Well, honey, the greatest number that fits the bill is the difference between the numbers. So, 6168 - 2447 = 3721, and 3118 - 2447 = 671. The greatest number that divides all three and leaves the same remainder is the greatest common divisor of 3721 and 671, which is 671.
5.2
26
56
No, 5 is not a factor of 42. A factor of a number divides it evenly with no remainder. When you divide 42 by 5, it does not divide evenly and leaves a remainder of 2. Therefore, 5 is not a factor of 42.
To determine factors of a number it is necessary to divide the number by prime numbers of increasing value. If there is no remainder then the prime number is a factor. The square root of 231 is approximately 15 so it is necessary to divide by all the prime numbers up to 13 (15 is not a prime number). 231 ÷ 2 leaves a remainder of 1 231 ÷ 3 divides exactly 77 times (which is 7 x 11 - both are prime numbers) 231 ÷ 5 leaves a remainder of 1 231 ÷ 7 divides exactly 33 times (which is 3 x 11 - both are prime numbers) 231 ÷ 11 divides exactly 21 times (which is 3 x 7 - both are prime numbers) 231 ÷ 13 leaves a remainder of 10 If we multiply together the three numbers that are shown to be factors 3 x 7 x 11 = 231 this confirms that there are no other factors of 231 except 1 and 231 itself. This last condition is true for every positive integer. 231 is divisible by 1, 3, 7, 11 and 231
The numbers that divide evenly by 7 and less than 75 are 7, 14, 21, 28, 35, 42, 49, 56, 63, and 70 Of the above numbers 56 when divided by 11 gives a quotient of 5 and a remainder of 1 Hence the number is 56
Let the greatest number be 'x'. Then nx + 7 = 742 : nx = 735 And mx + 7 = 1162 :mx = 1155 The number required is the Greatest Common Factor of 735 and 1155. 735 expressed as the product of its prime factors = 3 x 5 x 7 x 7 1155 expressed as the product of its prime factors = 3 x 5 x 7 x 11 The GCF is 3 x 5 x 7 = 105
Well, honey, the greatest number that fits the bill is the difference between the numbers. So, 6168 - 2447 = 3721, and 3118 - 2447 = 671. The greatest number that divides all three and leaves the same remainder is the greatest common divisor of 3721 and 671, which is 671.
3
It is an integer which, when divided by 2, leaves a remainder of 1.
5.2
26
No answer is possible as any number divided by 9 must either be exactly divisible by 9 or leave a remainder less than 9.
2