Highest Common Factor of 775, 921, 414 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 775, 921, 414 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 775, 921, 414 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 775, 921, 414 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 775, 921, 414 is 1.
HCF(775, 921, 414) = 1
HCF of 775, 921, 414 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 775, 921, 414 is 1.
Highest Common Factor of 775,921,414 is 1
Step 1: Since 921 > 775, we apply the division lemma to 921 and 775, to get
921 = 775 x 1 + 146
Step 2: Since the reminder 775 ≠ 0, we apply division lemma to 146 and 775, to get
775 = 146 x 5 + 45
Step 3: We consider the new divisor 146 and the new remainder 45, and apply the division lemma to get
146 = 45 x 3 + 11
We consider the new divisor 45 and the new remainder 11,and apply the division lemma to get
45 = 11 x 4 + 1
We consider the new divisor 11 and the new remainder 1,and apply the division lemma to get
11 = 1 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 775 and 921 is 1
Notice that 1 = HCF(11,1) = HCF(45,11) = HCF(146,45) = HCF(775,146) = HCF(921,775) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 414 > 1, we apply the division lemma to 414 and 1, to get
414 = 1 x 414 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 414 is 1
Notice that 1 = HCF(414,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 775, 921, 414 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 775, 921, 414?
Answer: HCF of 775, 921, 414 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 775, 921, 414 using Euclid's Algorithm?
Answer: For arbitrary numbers 775, 921, 414 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.