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 322, 854, 932 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 322, 854, 932 is 2 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 322, 854, 932 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 322, 854, 932 is 2.
HCF(322, 854, 932) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 322, 854, 932 is 2.
Step 1: Since 854 > 322, we apply the division lemma to 854 and 322, to get
854 = 322 x 2 + 210
Step 2: Since the reminder 322 ≠ 0, we apply division lemma to 210 and 322, to get
322 = 210 x 1 + 112
Step 3: We consider the new divisor 210 and the new remainder 112, and apply the division lemma to get
210 = 112 x 1 + 98
We consider the new divisor 112 and the new remainder 98,and apply the division lemma to get
112 = 98 x 1 + 14
We consider the new divisor 98 and the new remainder 14,and apply the division lemma to get
98 = 14 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 322 and 854 is 14
Notice that 14 = HCF(98,14) = HCF(112,98) = HCF(210,112) = HCF(322,210) = HCF(854,322) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 932 > 14, we apply the division lemma to 932 and 14, to get
932 = 14 x 66 + 8
Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 8 and 14, to get
14 = 8 x 1 + 6
Step 3: We consider the new divisor 8 and the new remainder 6, and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2, and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 14 and 932 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(932,14) .
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 322, 854, 932?
Answer: HCF of 322, 854, 932 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 322, 854, 932 using Euclid's Algorithm?
Answer: For arbitrary numbers 322, 854, 932 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.