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 962, 749, 108 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 962, 749, 108 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 962, 749, 108 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 962, 749, 108 is 1.
HCF(962, 749, 108) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 962, 749, 108 is 1.
Step 1: Since 962 > 749, we apply the division lemma to 962 and 749, to get
962 = 749 x 1 + 213
Step 2: Since the reminder 749 ≠ 0, we apply division lemma to 213 and 749, to get
749 = 213 x 3 + 110
Step 3: We consider the new divisor 213 and the new remainder 110, and apply the division lemma to get
213 = 110 x 1 + 103
We consider the new divisor 110 and the new remainder 103,and apply the division lemma to get
110 = 103 x 1 + 7
We consider the new divisor 103 and the new remainder 7,and apply the division lemma to get
103 = 7 x 14 + 5
We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get
7 = 5 x 1 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 962 and 749 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(103,7) = HCF(110,103) = HCF(213,110) = HCF(749,213) = HCF(962,749) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 108 > 1, we apply the division lemma to 108 and 1, to get
108 = 1 x 108 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 108 is 1
Notice that 1 = HCF(108,1) .
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 962, 749, 108?
Answer: HCF of 962, 749, 108 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 962, 749, 108 using Euclid's Algorithm?
Answer: For arbitrary numbers 962, 749, 108 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.