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 972, 611, 119 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 972, 611, 119 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 972, 611, 119 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 972, 611, 119 is 1.
HCF(972, 611, 119) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 972, 611, 119 is 1.
Step 1: Since 972 > 611, we apply the division lemma to 972 and 611, to get
972 = 611 x 1 + 361
Step 2: Since the reminder 611 ≠ 0, we apply division lemma to 361 and 611, to get
611 = 361 x 1 + 250
Step 3: We consider the new divisor 361 and the new remainder 250, and apply the division lemma to get
361 = 250 x 1 + 111
We consider the new divisor 250 and the new remainder 111,and apply the division lemma to get
250 = 111 x 2 + 28
We consider the new divisor 111 and the new remainder 28,and apply the division lemma to get
111 = 28 x 3 + 27
We consider the new divisor 28 and the new remainder 27,and apply the division lemma to get
28 = 27 x 1 + 1
We consider the new divisor 27 and the new remainder 1,and apply the division lemma to get
27 = 1 x 27 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 972 and 611 is 1
Notice that 1 = HCF(27,1) = HCF(28,27) = HCF(111,28) = HCF(250,111) = HCF(361,250) = HCF(611,361) = HCF(972,611) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 119 > 1, we apply the division lemma to 119 and 1, to get
119 = 1 x 119 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 119 is 1
Notice that 1 = HCF(119,1) .
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 972, 611, 119?
Answer: HCF of 972, 611, 119 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 972, 611, 119 using Euclid's Algorithm?
Answer: For arbitrary numbers 972, 611, 119 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.