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, 599, 72 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 972, 599, 72 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, 599, 72 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, 599, 72 is 1.
HCF(972, 599, 72) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 972, 599, 72 is 1.
Step 1: Since 972 > 599, we apply the division lemma to 972 and 599, to get
972 = 599 x 1 + 373
Step 2: Since the reminder 599 ≠ 0, we apply division lemma to 373 and 599, to get
599 = 373 x 1 + 226
Step 3: We consider the new divisor 373 and the new remainder 226, and apply the division lemma to get
373 = 226 x 1 + 147
We consider the new divisor 226 and the new remainder 147,and apply the division lemma to get
226 = 147 x 1 + 79
We consider the new divisor 147 and the new remainder 79,and apply the division lemma to get
147 = 79 x 1 + 68
We consider the new divisor 79 and the new remainder 68,and apply the division lemma to get
79 = 68 x 1 + 11
We consider the new divisor 68 and the new remainder 11,and apply the division lemma to get
68 = 11 x 6 + 2
We consider the new divisor 11 and the new remainder 2,and apply the division lemma to get
11 = 2 x 5 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 972 and 599 is 1
Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(68,11) = HCF(79,68) = HCF(147,79) = HCF(226,147) = HCF(373,226) = HCF(599,373) = HCF(972,599) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 72 > 1, we apply the division lemma to 72 and 1, to get
72 = 1 x 72 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 72 is 1
Notice that 1 = HCF(72,1) .
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, 599, 72?
Answer: HCF of 972, 599, 72 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 972, 599, 72 using Euclid's Algorithm?
Answer: For arbitrary numbers 972, 599, 72 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.