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, 856, 324, 109 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 985, 856, 324, 109 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, 856, 324, 109 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, 856, 324, 109 is 1.
HCF(985, 856, 324, 109) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 985, 856, 324, 109 is 1.
Step 1: Since 985 > 856, we apply the division lemma to 985 and 856, to get
985 = 856 x 1 + 129
Step 2: Since the reminder 856 ≠ 0, we apply division lemma to 129 and 856, to get
856 = 129 x 6 + 82
Step 3: We consider the new divisor 129 and the new remainder 82, and apply the division lemma to get
129 = 82 x 1 + 47
We consider the new divisor 82 and the new remainder 47,and apply the division lemma to get
82 = 47 x 1 + 35
We consider the new divisor 47 and the new remainder 35,and apply the division lemma to get
47 = 35 x 1 + 12
We consider the new divisor 35 and the new remainder 12,and apply the division lemma to get
35 = 12 x 2 + 11
We consider the new divisor 12 and the new remainder 11,and apply the division lemma to get
12 = 11 x 1 + 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 985 and 856 is 1
Notice that 1 = HCF(11,1) = HCF(12,11) = HCF(35,12) = HCF(47,35) = HCF(82,47) = HCF(129,82) = HCF(856,129) = HCF(985,856) .
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) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 109 > 1, we apply the division lemma to 109 and 1, to get
109 = 1 x 109 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 109 is 1
Notice that 1 = HCF(109,1) .
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, 856, 324, 109?
Answer: HCF of 985, 856, 324, 109 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 985, 856, 324, 109 using Euclid's Algorithm?
Answer: For arbitrary numbers 985, 856, 324, 109 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.