{"id":6583,"date":"2021-12-24T06:40:27","date_gmt":"2021-12-24T06:40:27","guid":{"rendered":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/?page_id=6583"},"modified":"2022-01-02T13:54:23","modified_gmt":"2022-01-02T13:54:23","slug":"factors-of-70-method-total-number-of-factors-mindspark","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/factors-of-70-method-total-number-of-factors-mindspark\/","title":{"rendered":"Factors of 70: Method, Total Number of Factors – Mindspark."},"content":{"rendered":"

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Factors of 70: Method, Total Number of Factors – Mindspark.<\/h1>\n

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What do we mean by Factors of 70?<\/strong><\/h2>\n

The factors of a number x\u00a0 are the numbers that completely divide x with zero as a remainder. It means that if y divides x and the remainder is 0 then we say that y is a factor of x.<\/span><\/p>\n

Factors of 70 i.e, the numbers which completely divide 70 are 1, 2, 5, 7,10, 14, 35, 70. Therefore 70 has a total of 8 factors.<\/span><\/p>\n

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Factors of 70<\/strong><\/h2>\n

The easiest way to calculate the factors of any number is by first dividing the number by its smallest factor. So the number which will divide the number completely and the quotient will be the factor(This is also known as Pair of the factors). We will repeat this process till we find all the factors.<\/span><\/p>\n

We know that 1 will the factor of every number, so\u00a0<\/span><\/p>\n

\\frac{70}{1}=70<\/span>, therefore\u00a0 1 and 70 will be the factors of 70. Now we\u2019ll do it with numbers greater than one.<\/span><\/p>\n

\\frac{70}{2}=35<\/span><\/span><\/p>\n

\\frac{70}{5}=14<\/span><\/span><\/span><\/p>\n

\\frac{70}{7}=10<\/span><\/span><\/span><\/p>\n

Therefore the factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70.<\/span><\/p>\n

 <\/p>\n

Factors of 70 by Tree Method<\/strong><\/h2>\n

The tree method is also known as Prime Factorisation. Prime Factorisation of a number means the way of writing the numbers by using its prime factors. For example, we can write 70 as 7 \u00d7 5 \u00d7 2.\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

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\"\"<\/span><\/p>\n

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We call it a tree method because the number of which we have to find the factors is the highest factor of itself (highest branch) and the rest of the factors are lower than the number itself and when we simplify it we get the prime numbers (which are circled in yellow in the figure) and this forms a shape like a tree as we are branching out 70 into its prime factors.<\/span><\/p>\n

70\u00a0 can be written with prime factorisation as-<\/span><\/p>\n

70 = 2 \u00d7 5<\/span> \u00d7 7<\/span><\/p>\n

 <\/p>\n

Factors of 70 in the form of Pairs<\/strong><\/h2>\n

We can write the factors in the form of pairs. The pair means that when we will multiply the two numbers well get the result as 70 –<\/span><\/p>\n

1 \u00d7 70 = 70<\/span><\/p>\n

2 \u00d7 35 = 70<\/span><\/p>\n

5 \u00d7 14 = 70<\/span><\/p>\n

7 \u00d7 10 = 70<\/span><\/p>\n

Therefore the Pairs are (1,70),(2,35),(5,14),(7,10).<\/span><\/p>\n

Factors of a number can be negative too but only when they are in pairs and negative as when we multiply the two numbers we get the result as 70.<\/span><\/p>\n

\u22121 \u00d7 \u221270 = 70<\/span><\/p>\n

\u22122 \u00d7 \u221235 = 70<\/span><\/p>\n

\u22125 \u00d7 \u221214 = 70<\/span><\/p>\n

\u22127 \u00d7 \u221210 = 70<\/span><\/strong><\/p>\n

Therefore the negative Pairs factor of 70 are (\u22121,\u221270),(\u22122,\u221235),(\u22125,\u221214),(\u22127,\u221210).<\/span><\/p>\n

 <\/p>\n

Examples\u00a0<\/strong><\/h2>\n

<\/strong><\/p>\n

1. Which of the following are factors of 70?<\/strong><\/p>\n

\u00a0 \u00a0 5,6,7,8,10,14\u00a0<\/strong><\/p>\n

Solution:<\/strong> 5,7,10 and 14 are factors of 70 as they completely divide 70.\u00a0<\/span><\/p>\n

6 and 8 are not factors of 70 as when we divide 70 from 6 and 8 we do not get natural numbers.<\/span><\/p>\n

70\/6 = 11.6\u00a0<\/span><\/p>\n

70\/8= 8.7<\/span><\/p>\n

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2. Is 140 a factor of 70?\u00a0<\/strong><\/p>\n

Solution:<\/strong> No, 140 is not a factor of 70. The highest factor of a number will be the number itself. 140 is a multiple of 70 as 70 x 2 = 140.<\/span><\/p>\n

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POINTS TO REMEMBER<\/strong><\/h2>\n