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, 867 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 972, 867 is 3 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, 867 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, 867 is 3.
HCF(972, 867) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 972, 867 is 3.
Step 1: Since 972 > 867, we apply the division lemma to 972 and 867, to get
972 = 867 x 1 + 105
Step 2: Since the reminder 867 ≠ 0, we apply division lemma to 105 and 867, to get
867 = 105 x 8 + 27
Step 3: We consider the new divisor 105 and the new remainder 27, and apply the division lemma to get
105 = 27 x 3 + 24
We consider the new divisor 27 and the new remainder 24,and apply the division lemma to get
27 = 24 x 1 + 3
We consider the new divisor 24 and the new remainder 3,and apply the division lemma to get
24 = 3 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 972 and 867 is 3
Notice that 3 = HCF(24,3) = HCF(27,24) = HCF(105,27) = HCF(867,105) = HCF(972,867) .
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, 867?
Answer: HCF of 972, 867 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 972, 867 using Euclid's Algorithm?
Answer: For arbitrary numbers 972, 867 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.