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, 13187 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 972, 13187 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, 13187 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, 13187 is 1.
HCF(972, 13187) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 972, 13187 is 1.
Step 1: Since 13187 > 972, we apply the division lemma to 13187 and 972, to get
13187 = 972 x 13 + 551
Step 2: Since the reminder 972 ≠ 0, we apply division lemma to 551 and 972, to get
972 = 551 x 1 + 421
Step 3: We consider the new divisor 551 and the new remainder 421, and apply the division lemma to get
551 = 421 x 1 + 130
We consider the new divisor 421 and the new remainder 130,and apply the division lemma to get
421 = 130 x 3 + 31
We consider the new divisor 130 and the new remainder 31,and apply the division lemma to get
130 = 31 x 4 + 6
We consider the new divisor 31 and the new remainder 6,and apply the division lemma to get
31 = 6 x 5 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 972 and 13187 is 1
Notice that 1 = HCF(6,1) = HCF(31,6) = HCF(130,31) = HCF(421,130) = HCF(551,421) = HCF(972,551) = HCF(13187,972) .
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, 13187?
Answer: HCF of 972, 13187 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 972, 13187 using Euclid's Algorithm?
Answer: For arbitrary numbers 972, 13187 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.