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, 987, 936 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 707, 987, 936 is 1 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, 987, 936 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, 987, 936 is 1.
HCF(707, 987, 936) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 707, 987, 936 is 1.
Step 1: Since 987 > 707, we apply the division lemma to 987 and 707, to get
987 = 707 x 1 + 280
Step 2: Since the reminder 707 ≠ 0, we apply division lemma to 280 and 707, to get
707 = 280 x 2 + 147
Step 3: We consider the new divisor 280 and the new remainder 147, and apply the division lemma to get
280 = 147 x 1 + 133
We consider the new divisor 147 and the new remainder 133,and apply the division lemma to get
147 = 133 x 1 + 14
We consider the new divisor 133 and the new remainder 14,and apply the division lemma to get
133 = 14 x 9 + 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 987 is 7
Notice that 7 = HCF(14,7) = HCF(133,14) = HCF(147,133) = HCF(280,147) = HCF(707,280) = HCF(987,707) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 936 > 7, we apply the division lemma to 936 and 7, to get
936 = 7 x 133 + 5
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 5 and 7, to get
7 = 5 x 1 + 2
Step 3: We consider the new divisor 5 and the new remainder 2, and apply the division lemma to get
5 = 2 x 2 + 1
We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7 and 936 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(936,7) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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, 987, 936?
Answer: HCF of 707, 987, 936 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 707, 987, 936 using Euclid's Algorithm?
Answer: For arbitrary numbers 707, 987, 936 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.