Highest Common Factor of 972, 545, 635 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, 545, 635 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 972, 545, 635 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, 545, 635 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, 545, 635 is 1.
HCF(972, 545, 635) = 1
HCF of 972, 545, 635 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, 545, 635 is 1.
Highest Common Factor of 972,545,635 is 1
Step 1: Since 972 > 545, we apply the division lemma to 972 and 545, to get
972 = 545 x 1 + 427
Step 2: Since the reminder 545 ≠ 0, we apply division lemma to 427 and 545, to get
545 = 427 x 1 + 118
Step 3: We consider the new divisor 427 and the new remainder 118, and apply the division lemma to get
427 = 118 x 3 + 73
We consider the new divisor 118 and the new remainder 73,and apply the division lemma to get
118 = 73 x 1 + 45
We consider the new divisor 73 and the new remainder 45,and apply the division lemma to get
73 = 45 x 1 + 28
We consider the new divisor 45 and the new remainder 28,and apply the division lemma to get
45 = 28 x 1 + 17
We consider the new divisor 28 and the new remainder 17,and apply the division lemma to get
28 = 17 x 1 + 11
We consider the new divisor 17 and the new remainder 11,and apply the division lemma to get
17 = 11 x 1 + 6
We consider the new divisor 11 and the new remainder 6,and apply the division lemma to get
11 = 6 x 1 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 972 and 545 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(11,6) = HCF(17,11) = HCF(28,17) = HCF(45,28) = HCF(73,45) = HCF(118,73) = HCF(427,118) = HCF(545,427) = HCF(972,545) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 635 > 1, we apply the division lemma to 635 and 1, to get
635 = 1 x 635 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 635 is 1
Notice that 1 = HCF(635,1) .
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, 545, 635 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, 545, 635?
Answer: HCF of 972, 545, 635 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 972, 545, 635 using Euclid's Algorithm?
Answer: For arbitrary numbers 972, 545, 635 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
