Highest Common Factor of 105, 722, 324 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 105, 722, 324 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 105, 722, 324 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 105, 722, 324 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 105, 722, 324 is 1.
HCF(105, 722, 324) = 1
HCF of 105, 722, 324 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 105, 722, 324 is 1.
Highest Common Factor of 105,722,324 is 1
Step 1: Since 722 > 105, we apply the division lemma to 722 and 105, to get
722 = 105 x 6 + 92
Step 2: Since the reminder 105 ≠ 0, we apply division lemma to 92 and 105, to get
105 = 92 x 1 + 13
Step 3: We consider the new divisor 92 and the new remainder 13, and apply the division lemma to get
92 = 13 x 7 + 1
We consider the new divisor 13 and the new remainder 1, and apply the division lemma to get
13 = 1 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 105 and 722 is 1
Notice that 1 = HCF(13,1) = HCF(92,13) = HCF(105,92) = HCF(722,105) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 324 > 1, we apply the division lemma to 324 and 1, to get
324 = 1 x 324 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 324 is 1
Notice that 1 = HCF(324,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 105, 722, 324 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 105, 722, 324?
Answer: HCF of 105, 722, 324 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 105, 722, 324 using Euclid's Algorithm?
Answer: For arbitrary numbers 105, 722, 324 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.