Highest Common Factor of 972, 699, 951 using Euclid's algorithm
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, 699, 951 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 972, 699, 951 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, 699, 951 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, 699, 951 is 3.
HCF(972, 699, 951) = 3
HCF of 972, 699, 951 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 972, 699, 951 is 3.
Highest Common Factor of 972,699,951 is 3
Step 1: Since 972 > 699, we apply the division lemma to 972 and 699, to get
972 = 699 x 1 + 273
Step 2: Since the reminder 699 ≠ 0, we apply division lemma to 273 and 699, to get
699 = 273 x 2 + 153
Step 3: We consider the new divisor 273 and the new remainder 153, and apply the division lemma to get
273 = 153 x 1 + 120
We consider the new divisor 153 and the new remainder 120,and apply the division lemma to get
153 = 120 x 1 + 33
We consider the new divisor 120 and the new remainder 33,and apply the division lemma to get
120 = 33 x 3 + 21
We consider the new divisor 33 and the new remainder 21,and apply the division lemma to get
33 = 21 x 1 + 12
We consider the new divisor 21 and the new remainder 12,and apply the division lemma to get
21 = 12 x 1 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 972 and 699 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(21,12) = HCF(33,21) = HCF(120,33) = HCF(153,120) = HCF(273,153) = HCF(699,273) = HCF(972,699) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 951 > 3, we apply the division lemma to 951 and 3, to get
951 = 3 x 317 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 951 is 3
Notice that 3 = HCF(951,3) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 972, 699, 951 using Euclid's Algorithm
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, 699, 951?
Answer: HCF of 972, 699, 951 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 972, 699, 951 using Euclid's Algorithm?
Answer: For arbitrary numbers 972, 699, 951 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.