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 640, 777, 66, 437 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 640, 777, 66, 437 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 640, 777, 66, 437 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 640, 777, 66, 437 is 1.
HCF(640, 777, 66, 437) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 640, 777, 66, 437 is 1.
Step 1: Since 777 > 640, we apply the division lemma to 777 and 640, to get
777 = 640 x 1 + 137
Step 2: Since the reminder 640 ≠ 0, we apply division lemma to 137 and 640, to get
640 = 137 x 4 + 92
Step 3: We consider the new divisor 137 and the new remainder 92, and apply the division lemma to get
137 = 92 x 1 + 45
We consider the new divisor 92 and the new remainder 45,and apply the division lemma to get
92 = 45 x 2 + 2
We consider the new divisor 45 and the new remainder 2,and apply the division lemma to get
45 = 2 x 22 + 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 640 and 777 is 1
Notice that 1 = HCF(2,1) = HCF(45,2) = HCF(92,45) = HCF(137,92) = HCF(640,137) = HCF(777,640) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 66 > 1, we apply the division lemma to 66 and 1, to get
66 = 1 x 66 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 66 is 1
Notice that 1 = HCF(66,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 437 > 1, we apply the division lemma to 437 and 1, to get
437 = 1 x 437 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 437 is 1
Notice that 1 = HCF(437,1) .
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 640, 777, 66, 437?
Answer: HCF of 640, 777, 66, 437 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 640, 777, 66, 437 using Euclid's Algorithm?
Answer: For arbitrary numbers 640, 777, 66, 437 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.