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 985, 558, 342, 229 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 985, 558, 342, 229 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 985, 558, 342, 229 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 985, 558, 342, 229 is 1.
HCF(985, 558, 342, 229) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 985, 558, 342, 229 is 1.
Step 1: Since 985 > 558, we apply the division lemma to 985 and 558, to get
985 = 558 x 1 + 427
Step 2: Since the reminder 558 ≠ 0, we apply division lemma to 427 and 558, to get
558 = 427 x 1 + 131
Step 3: We consider the new divisor 427 and the new remainder 131, and apply the division lemma to get
427 = 131 x 3 + 34
We consider the new divisor 131 and the new remainder 34,and apply the division lemma to get
131 = 34 x 3 + 29
We consider the new divisor 34 and the new remainder 29,and apply the division lemma to get
34 = 29 x 1 + 5
We consider the new divisor 29 and the new remainder 5,and apply the division lemma to get
29 = 5 x 5 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 985 and 558 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(29,5) = HCF(34,29) = HCF(131,34) = HCF(427,131) = HCF(558,427) = HCF(985,558) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 342 > 1, we apply the division lemma to 342 and 1, to get
342 = 1 x 342 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 342 is 1
Notice that 1 = HCF(342,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 229 > 1, we apply the division lemma to 229 and 1, to get
229 = 1 x 229 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 229 is 1
Notice that 1 = HCF(229,1) .
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 985, 558, 342, 229?
Answer: HCF of 985, 558, 342, 229 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 985, 558, 342, 229 using Euclid's Algorithm?
Answer: For arbitrary numbers 985, 558, 342, 229 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.