Highest Common Factor of 991, 684, 224 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 991, 684, 224 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 991, 684, 224 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 991, 684, 224 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 991, 684, 224 is 1.
HCF(991, 684, 224) = 1
HCF of 991, 684, 224 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 991, 684, 224 is 1.
Highest Common Factor of 991,684,224 is 1
Step 1: Since 991 > 684, we apply the division lemma to 991 and 684, to get
991 = 684 x 1 + 307
Step 2: Since the reminder 684 ≠ 0, we apply division lemma to 307 and 684, to get
684 = 307 x 2 + 70
Step 3: We consider the new divisor 307 and the new remainder 70, and apply the division lemma to get
307 = 70 x 4 + 27
We consider the new divisor 70 and the new remainder 27,and apply the division lemma to get
70 = 27 x 2 + 16
We consider the new divisor 27 and the new remainder 16,and apply the division lemma to get
27 = 16 x 1 + 11
We consider the new divisor 16 and the new remainder 11,and apply the division lemma to get
16 = 11 x 1 + 5
We consider the new divisor 11 and the new remainder 5,and apply the division lemma to get
11 = 5 x 2 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 991 and 684 is 1
Notice that 1 = HCF(5,1) = HCF(11,5) = HCF(16,11) = HCF(27,16) = HCF(70,27) = HCF(307,70) = HCF(684,307) = HCF(991,684) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 224 > 1, we apply the division lemma to 224 and 1, to get
224 = 1 x 224 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 224 is 1
Notice that 1 = HCF(224,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 991, 684, 224 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 991, 684, 224?
Answer: HCF of 991, 684, 224 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 991, 684, 224 using Euclid's Algorithm?
Answer: For arbitrary numbers 991, 684, 224 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.