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 368, 648, 77 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 368, 648, 77 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 368, 648, 77 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 368, 648, 77 is 1.
HCF(368, 648, 77) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 368, 648, 77 is 1.
Step 1: Since 648 > 368, we apply the division lemma to 648 and 368, to get
648 = 368 x 1 + 280
Step 2: Since the reminder 368 ≠ 0, we apply division lemma to 280 and 368, to get
368 = 280 x 1 + 88
Step 3: We consider the new divisor 280 and the new remainder 88, and apply the division lemma to get
280 = 88 x 3 + 16
We consider the new divisor 88 and the new remainder 16,and apply the division lemma to get
88 = 16 x 5 + 8
We consider the new divisor 16 and the new remainder 8,and apply the division lemma to get
16 = 8 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 368 and 648 is 8
Notice that 8 = HCF(16,8) = HCF(88,16) = HCF(280,88) = HCF(368,280) = HCF(648,368) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 77 > 8, we apply the division lemma to 77 and 8, to get
77 = 8 x 9 + 5
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 5 and 8, to get
8 = 5 x 1 + 3
Step 3: We consider the new divisor 5 and the new remainder 3, and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 8 and 77 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(77,8) .
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 368, 648, 77?
Answer: HCF of 368, 648, 77 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 368, 648, 77 using Euclid's Algorithm?
Answer: For arbitrary numbers 368, 648, 77 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.