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 117, 777 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 117, 777 is 3 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 117, 777 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 117, 777 is 3.
HCF(117, 777) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 117, 777 is 3.
Step 1: Since 777 > 117, we apply the division lemma to 777 and 117, to get
777 = 117 x 6 + 75
Step 2: Since the reminder 117 ≠ 0, we apply division lemma to 75 and 117, to get
117 = 75 x 1 + 42
Step 3: We consider the new divisor 75 and the new remainder 42, and apply the division lemma to get
75 = 42 x 1 + 33
We consider the new divisor 42 and the new remainder 33,and apply the division lemma to get
42 = 33 x 1 + 9
We consider the new divisor 33 and the new remainder 9,and apply the division lemma to get
33 = 9 x 3 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 117 and 777 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(33,9) = HCF(42,33) = HCF(75,42) = HCF(117,75) = HCF(777,117) .
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 117, 777?
Answer: HCF of 117, 777 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 117, 777 using Euclid's Algorithm?
Answer: For arbitrary numbers 117, 777 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.