Highest Common Factor of 707, 301 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 707, 301 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 707, 301 is 7 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 707, 301 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 707, 301 is 7.
HCF(707, 301) = 7
HCF of 707, 301 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 707, 301 is 7.
Highest Common Factor of 707,301 is 7
Step 1: Since 707 > 301, we apply the division lemma to 707 and 301, to get
707 = 301 x 2 + 105
Step 2: Since the reminder 301 ≠ 0, we apply division lemma to 105 and 301, to get
301 = 105 x 2 + 91
Step 3: We consider the new divisor 105 and the new remainder 91, and apply the division lemma to get
105 = 91 x 1 + 14
We consider the new divisor 91 and the new remainder 14,and apply the division lemma to get
91 = 14 x 6 + 7
We consider the new divisor 14 and the new remainder 7,and apply the division lemma to get
14 = 7 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 707 and 301 is 7
Notice that 7 = HCF(14,7) = HCF(91,14) = HCF(105,91) = HCF(301,105) = HCF(707,301) .
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Frequently Asked Questions on HCF of 707, 301 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 707, 301?
Answer: HCF of 707, 301 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 707, 301 using Euclid's Algorithm?
Answer: For arbitrary numbers 707, 301 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.